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T. Adachi and T. Sunada, Twisted Perron-Probenius theorem and L-functions, J. Fnal. Anal. 71 (1987) 1–46.
O. Agam, The magnetic response of chaotic mesoscopic systems, J. Phys. I Fr. 4 (1994) 697–730.
L. Ahlfors, Some remarks on Teichmüller’s space of Riemann surfaces, Ann. Math. 74 (1961) 71.
Y. Alhassid and R. Levine, Spectral autocorrelation function in the statistical theory of energy levels, Phys. Rev. A46 (1992) 4650–4653.
D. Alonso and P. Gaspard, Role of the edge orbits in the semiclassical quantization of the stadium billiard, J. Phys. A27 (1994) 1599–1607.
H. Alt, P. v. Brentano, H. Gräf, et al., Precision test of the Breit-Wigner formula on resonances in a superconducting microwave cavity, (preprint, 1995).
H. Alt, H. Gräf, H. Harney, et al., GOE-statistics in a microwave stadium billiard with chaotic dynamics: Porter-Thomas distribution and algebraic decay ofr time correlations, Phys. Rev. Lett. 74 (1995) 62.
H. Alt, H. Gräf, H. Harney, et al., Superconducting billiard cavities with chaotic dynamics — an experimental test of statistical measures, (preprint, 1995).
H. Alt, H. Gräf, H. Harney, et al., Decay of the classical Bunimovich stadium, (preprint, 1995).
H. Alt, H. Gräf, R. Hofferbert, et al., Studies of chaotic dynamics in a three-dimensional superconducting microwave billiard, (preprint, 1996).
B. L. Al’tshuler, Pis’ma Zh. Eksp. Teor. Fiz. 41 (1985) 530;
B. L. Al’tshuler, JETP Lett. 41 (1985) 648.
B. L. Al’tshuler and D. E. Khmel’nitskii, JETP Lett. 42 (1986) 359.
B. L. Al’tshuler and B. I. Shklovskii, Repulsion of energy levels and conductivity of small metal samples, Zh. Eksp. Teor. Fiz. 91 (1986) 220;
B. L. Al’tshuler and B. I. Shklovskii, Sov. Phys. JETP 64 (1986) 127–135.
M. Antoine, A. Comtet, and S. Ouvry, Scattering on a hyperbolic torus in a constant magnetic field, J. Phys. A23 (1990) 3699–3710.
N. Argaman, E. Doron, J. Keating, A. Kitaev, M. Sieber and U. Smilansky, Correlation in the actions of periodic orbits derived from quantum chaos, Phys. Rev. Lett. 71 (1993) 4326–4329.
N. Argaman, Y. Imry and U. Smilansky, Semiclassical analysis of spectral correlations in mesoscopic theory, Phys. Rev. B47 (1993) 4440–4457.
E. Artin, Ein mechanisches system mit quasiergodischen bahnen, Abh. Math. Sem. Univ. Hamburg, 3 (1924) 170–175.
A. O. L. Atkin and J. Lehner, Hecke operators on Γ0 (m), Math. Ann. 185 (1970) 134–160.
E. Aurell and C. Itzykson, Rational billiards and algebraic curves, JGP 5 (1988) 191–208.
R. Aurich, A. Bäcker and F. Steiner, Mode fluctuations as fingprint of chaotic and non-chaotic systems, (preprint, 1996).
R. Aurich, E. Bogomolny, and F. Steiner, Periodic orbits in the regular hyperbolic octagon, Physica D48 (1991) 91–101.
R. Aurich, J. Bolte and F. Steiner, Universal signatures of quantum chaos, Phys. Rev. Lett. 73 (1994) 1356–1359.
R. Aurich, J. Bolte, C. Matthies, M. Sieber, and F. Steiner, Crossing the entropy barrier of dynamical zeta functions, Physica D63 (1993) 71–86.
R. Aurich, T. Hesse, and F. Steiner, Role of nonperiodic orbits in semiclassical quantization of the truncated hyperbola billiard, Phys. Rev. Lett. 74 (1995) 4408–4411.
R. Aurich and J. Marklof, Trace formulae for three-dimensional hyperbolic lattices and application to a strongly chaotic tetrahedral billiard, Physica D92 (1996) 101.
R. Aurich, F. Scheffler and F. Steiner, Subtleties of arithmetical quantum chaos, Phys. Rev. E51 (1995) 4173–4189.
R. Aurich, M. Sieber and F. Steiner, Quantum chaos of the Hadamard-Gutzwiller model, Phys. Rev. Lett. 61 (1988) 483–487.
R. Aurich and F. Steiner, On the periodic orbits of a strongly chaotic system, Physica D32 (1988) 451–460.
R. Aurich and F. Steiner, Energy-level statistics of the Hadamard-Gutzwiller ensemble, Physica D43 (1990) 155–180.
R. Aurich and F. Steiner, Staircase functions, spectral rigidity, and a rule for quantizing chaos, Phys. Rev. A45 (1992) 583–592.
R. Aurich and F. Steiner, Statistical properties of highly excited quantum eigenstates of a strongly chaotic system, Physica D64 (1993) 185–214.
R. Aurich and F. Steiner, Periodic-orbit theory of the number variance Σ2(L) of strongly chaotic systems, Physica D82 (1995) 266–287.
R. Aurich and F. Steiner, Quantum eigenstates of a strongly chaotic system and the scar phenomenon, Chaos, Sol. Frac. 5 (1995) 229–255.
J. E. Avron, M. Klein, A. Pneuli, and L. Sadun, Hall conductance and adiabatic charge transport of leaky tori, Phys. Rev. Lett. 69 (1992) 128–131.
J. E. Avron and A. Pneuli, Landau Hamiltonians on symmetric spaces, in Ideas and Methods in Quantum and Statistical Physics, ed. S. Albeverio et al., vol. 2 (Cambridge University Press, Cambridge, 1992) 96–117.
A. Bäcker and H. Dullin, Symbolic dynamics and periodic orbits for the cardioid billiard, (preprint, 1995).
A. Bäcker, F. Steiner and P. Stifter, Spectral statistics in the quantized cardioid billiard, Phys. Rev. E52 (1993) 2463–2472.
V. Baladi, Dynamical zeta functions, (preprint, 1993).
N. L. Balazs and A. Voros, Chaos on the pseudosphere, Phys. Rep. 143 (1986) 109–240.
R. Balian and C. Bloch, Solution of the Schrodinger equation in terms of classical paths, Ann. Phys. 85 (1974) 514.
R. Balian and C. Bloch, Distribution of eigenfrequencies for the wave function in a finite domain, III, Eigenfrequency density oscillations, Ann. Phys. 69 (1972) 76–160.
H. P. Baltes and E. R. Hilf, Spectra of Finite Systems (Bibliographisches Institut, Mannheim, 1976).
B. L. Al’tshuler and B. I. Shklovskii, Weak-localization and integrability in ballistic cavities, (preprint, 1992).
H. Baranger, R. Jalabert, and A. Stone, Quantum-chaotic scattering effects in semiconductor microstructures, Chaos 3 (1993) 665–682.
H. U. Baranger and P. A. Mello, Mesoscopic transport through chaotic cavities: a random S-matrix theory approach, Phys. Rev. Lett. 73 (1994) 142–145.
H. Baranger and P. Mello, How phase-breaking affects quantum transport through chaotic cavities, (preprint, 1994).
H. Baranger and P. Mello, Reflection symmetric ballistic microstructures: quantum transport properties, (preprint, 1996).
H. Baranger and A. Stone, Quenching of the Hall resistance in ballistic microstructures: a collimation effect, Phys. Rev. Lett. 63 (1989) 414–417.
C. W. J. Beenakker, Universal limit of critical-current fluctuations in mesoscopic Josephson junctions, Phys Rev. Lett. 67 (1991) 3836–3839.
C. W. J. Beenakker, Quantum transport in semiconductor-superconductor microjunctions, Phys. Rev. B46 (1992) 12841–12
C. W. J. Beenakker, Universality in random-matrix theory of quantum transport, Phys. Rev. Lett. 70 (1993) 1155–1158.
C. W. J. Beenakker, Random-matrix theory of mesoscopic fluctuations in conductors and superconductors, Phys. Rev. B47 (1993) 15763–15775.
C. W. J. Beenakker, Universality of weak localization in disordered wires, Phys. Rev. B49 (1994) 2205–2207.
C. W. J. Beenakker and M. Biittiker, Suppression of shot noise in metallic diffusive conductors, Phys. Rev. B46 (1992) 1889–1892.
C. W. J. Beenakker and B. Rejaei, Nonlogarithmic repulsion of transmission eigenvalues in disordered wire, Phys. Rev. Lett. 71 (1993) 3689–3692.
C. W. J. Beenakker and B. Rejaei, Random-matrix theory of parametric correlations in the spectra of disordered metals and chaotic billiards, Physica A203 (1994) 61–90.
C. W. J. Beenakker and H. van Houten, Billiard model of a ballistic multiprobe conductor, Phys. Rev. Lett. 63 (1989) 1857–1860.
G. Benettin and J. M. Stelcyn, Numerical experiments on the free motion of a point mass moving in a plane convex region, Phys. Rev A17 (1978) 773–785.
P. Bérard, On the wave equation on a compact Riemannian manifold without conjugate points, Math. Z. 155 (1977) 249–276.
P. Bérard, Varietes Riemanniennes isospectrales non isometriques, Asterisque 177–178 (1989) 127–154.
P. Bérard, Transplantation et isospectralite, Math. Ann. 292 (1992) 547–559.
M. Berry, J. Katine, C. Marcus, R. Westervelt and A. Gossard, Weak localization and conductance fluctuations in a chaotic quantum dot, Surf. Sci. 305 (1994) 495–500.
M. V. Berry, Regular and irregular semiclassical wavefunctions, J. Phys. A10 (1977) 2083–2091; see also Phil. Trans. Roy. Soc. A287 (1977) 237–271.
M. V. Berry, Regularity and chaos in classical mechanics, illustrated by three deformations of a circular billiard, Eur. J. Phys 2 (1981) 91–102.
M. V. Berry, Quantizing a classically ergodic system: Sinai’s billiard and the KKR method, Ann. Phys. 131 (1981) 163–216.
M. V. Berry, Chaotic behavior of deterministic systems. Les Houches Lectures XXXVI (ed. G. Iooss, R. Helleman and R. Stora, North-Holland, Amsterdam, 1983) 171–271.
M. V. Berry, Semiclassical theory of spectral rigidity, Proc. Roy. Soc. London A400 (1985) 229–251.
M. V. Berry, Riemann’s zeta function: a model for quantum chaos? in Quantum Chaos and Statistical Nuclear Physics, ed. T. H. Seligman and H. Nishioka (Lecture Notes in Physics, 263, Springer, Berlin, 1986), 1–17.
M. V. Berry, Quantum chaology, Proc. Roy. Soc. A413 (1987) 183–198.
M. V. Berry, Semiclassical formula for the number variance of the Riemann zeros, Nonlinearity 1 (1988) 399–407.
M. V. Berry, Quantum scars of classical closed orbits in phase space, Proc. Roy. Soc. London A423 (1989) 219–231.
M. V. Berry, Some quantum-to-classical asymptotics, in Chaos and Quantum Physics: Les Houches Lecture Series 52 (ed. M.-J. Giannoni, A. Voros, and J. Zinn-Justin, North-Holland, Amsterdam, 1991).
M. V. Berry and J. Keating, Persistent current flux correlations calculated by quantum chaology, J. Phys. A 27 (1994) 6167–6176.
M. V. Berry and R. Mondragon, Proc. Roy. Soc. A412 (1987) 53–74.
M. V. Berry and M. Robnik, Statistics of energy levels without time-reversal symmetry: Aharonov-Bohm chaotic billiards, J. Phys. A19 (1986) 649–668.
M. V. Berry and M. Tabor, Closed orbits and the regular bound spectrum, Proc. Roy. Soc. Lond. A349 (1976) 101–123.
M. V. Berry and M. Tabor, Level clustering in the regular spectrum, Proc. Roy. Soc. London A356 (1977) 375–394.
M. V. Berry and M. Tabor, Calculating the bound spectrum by path summation in action-angle variables, J. Phys. A 10 (1977) 371–379.
M. V. Berry and M. Wilkinson, Diabolical points in the spectra of triangles, Proc. Roy. Soc. London A392 (1984) 15–43.
S. de Bierve and A. Bouzouina, Equipartition of the eigenfunctions of quantized ergodic maps on the torus, (preprint, 1995).
D. Biswas and S. Jain, Quantum description of a pseudointegrable system: the 7r/3-rhombus billiard, Phys. Rev. A42 (1990) 3170–3185.
D. Biswas and S. Sinha, Theory of fluctuations in pseudointegrable systems, Phys. Rev. Lett. 70 (1993) 916–919.
P. Bleher, The energy level spacing for two harmonic oscillators with generic ratio of frequencies, J. Stat. Phys. 63 (1991) 261–283.
P. Bleher, Quasiclassical expansion and the problem of quantum chaos, LNM 1469 (1991) 60–89.
P. Bleher, On the distribution of the number of lattice points inside a family of convex ovals, Duke Math. J. 67 (1992) 461–481.
P. Bleher, Distribution of the error term in the Weyl asymptotics for the Laplace operator on a two-dimensional torus and related lattice problems, Duke Math. J. 70 (1993) 655–682.
P. Bleher, Trace formula for quantumn integrable systems, lattice-point problem and small divisors, (preprint, 1996).
P. Bleher, Z. Cheng, F. Dyson, J. Lebowitz, Distribution of the error term for the number of lattice points inside a shifted circle, Comm. Math. Phys. 154 (1993) 433–469.
P. Bleher, F. Dyson and J. Lebowitz, Non-Gaussian energy level statistics for some integrable systems, Phys. Rev. Lett. 71 (1993) 3047–3050.
P. Bleher, D. Kosygin and Ya. Sinai, Distribution of enery levels of quantum free particle on the Liouville surface and trace formulae, Comm. Math. Phys. 170 (1995) 375–403.
P. Bleher and J. Lebowitz, Energy-level statistics of model quantum systems: universality and scaling in a lattice-point problem, J. Stat. Phys. 74 (1994) 167–217.
P. Bleher and J. Lebowitz, Variance of number of lattice points in random narrow elliptic strip, Ann. Inst. H. Poincare 31 (1995) 27–58.
S. Bochner, On Riemann’s functional equation with multiple gamma factors, Ann. Math. 67 (1958) 29–41.
E. B. Bogomolny, B. Georgeot, M.-J. Giannoni and C. Schmit, Chaotic billiards generated by arithmetic groups, Phys. Rev. Lett. 69 (1992) 1477–1480.
E. B. Bogomolny, B. Georgeot, M.-J. Giannoni and C. Schmit, Arithmetical chaos, (preprint, 1993).
E. B. Bogomolny, B. Georgeot, M.-J. Giannoni and C. Schmit, Quantum chaos on constant negative curvature surface, Chaos, Solitons & Fractals 5 (1995) 1311–1323.
E. B. Bogomolny, B. Georgeot, M.-J. Giannoni and C. Schmit, Trace formulas for arithmetical systems, Phys. Rev. E47 (1993) R2217.
E. Bogomolny and J. Keating, Random matrix theory and the Riemann zeros I: three and four-point correlations, Nonlin. 8 (1995) 1115–1131.
E. Bogomolny and P. Leboeuf, Statistical properties of the zeros of zeta functions — beyond the Riemann case, Nonlin. 7 (1994) 1155–1167.
E. Bogomolny, F. Leyvraz, and C. Schmit, Distribution of eigenvalues for the modular group, Comm. Math. Phys. 176 (1996) 577–617.
O. Bohigas, Random matrix theories and chaotic dynamics, in Chaos and Quantum Physics, M. J. Giannoni et al., eds. (Elsevier, Amsterdam, 1991) 89–199.
O. Bohigas, M.-J. Giannoni and C. Schmit, Characterization of chaotic quantum spectra and universality of level fluctuation laws, Phys. Rev. Lett. 52 (1984) 1–4;
O. Bohigas, M.-J. Giannoni and C. Schmit, Spectral properties of the Laplacian and random matrix theory, J. Physique Lett. 45 (1984) L1015.
O. Bohigas, M.-J. Giannoni and C. Schmit, Spectral fluctuations, random matrix theory and chaotic motion, Lecture Notes in Physics 262 (1986).
C. Boldrighini, M. Keane and F. Marchetti, Billiards in polygons, Ann. Prob. 6 (1978) 532–540.
J. Bolte, Some studies on arithmetical chaos in classical and quantum mechanics, Inter. J. Mod. Phys. B7 (1993) 4451–4553.
J. Bolte, Periodic orbits in arithmetical chaos on hyperbolic surfaces, Nonlin. 6 (1993) 935–951.
J. Bolte, G. Steil and F. Steiner, Arithmetical chaos and violation of universality in energy level statistics, Phys. Rev. Lett. 69 (1992) 2188–2191.
E. Bombieri and D. Hejhal, Sur les zeros des fonctions zeta d’Epstein, CRAS 304 (1987) 213–217.
E. Bombieri and D. Hejhal, On the distribution of zeros of linear combination of Euler products, Duke Math. J. 80 (1995) 821–862.
M. Boshernitzan, G. Galperin, T. Kruger and S. Troubetzkoy, Periodic billiard orbits are dense in rational polygons, (preprint, 1996).
A. Bouzouina and S. De Bievre, Equipartition of the eigenvunctions of quantized ergodic maps on the torus, (preprint, 1996).
R. Bowen, The equidistribution theory of closed geodesics, Amer. J. Math. 94 (1972) 413–423.
O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics I (Springer-Verlag, New York, 1979).
R. Brooks, On manifolds of negative curvature with isospectral potentials, Top. 26 (1987) 63–66.
R. Brooks, P. Perry and P. Yang, Isospectral sets of conformally equivalent metrics, Duke Math. J. 58 (1989) 131–150.
P. W. Brouwer and C. W. J. Beenakker, Conductance distribution of a quantum dot with non-ideal single-channel leads, preprint, 1993.
R. Brummelhuis, T. Paul and A. Uribe, Spectral estimates around a critical level, Duke Math. J. 78 (1995) 477–530.
L. Bunimovich, On the ergodic properties of some billiards, Fun. Anal. Appl. 8 (1974) 73–74.
L. Bunimovich, On the ergodic properties of nowhere dispersing billiards, Comm. Math. Phys. 65 (1979) 295–312.
P. Buser, Riemannsche flachen mit eigenwerten in (0,1/4), Comm. Math. Helv. 52 (1977) 25–34.
P. Buser, Geometry and Spectra of Compact Riemannian Surfaces (Birkhauser, Boston, 1992).
P. Buser, J. Conway, P. Doyle and K. Semmler, Some planar isospectral domains, Int. Math. Res. Not.
M. Biittiker, Scattering theory of thermal and excess noise in open conductors, Phys. Rev. Lett. 65 (1990) 2901–2904.
H. Bruus and N. Whelan, Periodic orbit theory of edge diffraction, (preprint, 1995).
G. Casati, B. Chirikov and I. Guarneri, Energy-level statistics of integrable quantum systems, Phys. Rev. Lett. 54 (1985) 1350–1353.
G. Casati, I. Guarneri and F. Valz-Gris, Degree of randomness of the sequence of eigenvalues, Phys. Rev. A30 (1984) 1586–1588.
J. T. Chalker and A. M. S. Macêdo, Complete characterization of universal fluctuations in quasi-one-dimensional mesoscopic conductivity, Phys. Rev. Lett. 71 (1993) 3693.
K. Chandrasekharan and R. Narasimhan, Zeta-functions of ideal classes in quadratic fields and zeros on the critical line, Comm. Math. Helv. 43 (1968) 18–30.
A. Chang, H. Baranger, L. Pfeiffer and K. West, Weak-localization in chaotic versus non-chaotic cavities: a striking difference in the line shape, Phys. Rev. Lett. 73 (1994) 2111.
Z. Cheng and J. Lebowitz, Statistics of energy levels in integrable quantum systems, Phys. Rev. A44 (1991) R3399-R3402.
Z. Cheng, J. Lebowitz and P. Major, On the number of lattice points between two enlarged and randomly shifted copies of an oval, Prob. Thy. Rel. Fields 100 (1994) 253–268.
T. Cheon and T. Cohen, quantum level statistics of pseudointegrable billiards, Phys. Rev. Lett. 62 (1989) 2769–2772.
N. Chernoff, Ergodic and statistical properties of peicewise linear hyperbolic automorphism of the two-torus, J. Stat. Phys. 69 (1992) 111–134.
N. Chernov and C. Haskell, Nonuniformly hyperbolic K-systems are Bernoulli, (preprint, 1994).
B. A. Cipra, On the Niwa-Shintani theta-kernel lifting of modular forms, Nagoya Math. J. 91 (1983) 49–117.
H. Cohen and J. Oesterle, Dimensions des espaces de formes modulaires, International Summer School on Modular Functions (1976), LNM 627, 69–78.
Y. Colin de Verdière, Spectre du Laplacien et longeurs des geodesiques periodiques I, II, Compos. Math. 27 (1973) 83–106, 159–184.
Y. Colin de Verdière, Nombre de points entiers dans une famille homo-thetique de domaines de Rn, Ann. Sci. Ec. Norm. Sup. 10 (1977) 559–576.
Y. Colin de Verdiere, Spectra conjoint d’operateurs pseudo-differentiels qui communtent II. Le cas integrable, Math. Z. 171 (1980) 51–73.
Y. Colin de Verdière, Une formule de trace pour l’operateur de Schrödinger dans R3, Annales de l’ENS 14 (1981).
Y. Colin de Verdière, Pseudo Laplacians, Ann. Inst. Fourier 32 (1982) 275–286.
Y. Colin de Verdière, Pseudo-Laplaciens, II, Ann. Inst. Fourier 33 (1983) 87–113.
Y. Colin de Verdière, Sur les longueurs des trajectories periodiques d’un billiard, in Geometrie Symplectique et de Contact (Hermann, Paris, 1984) 122–139.
Y. Colin de Verdière, Ergodicité et fonctions propres du Laplacien, Comm. Math. Phys. 102 (1985) 497–502.
Y. Colin de Verdière, Theorie spectrale des surfaces de Riemann d’aire infinie, Asterisque 132 (1985) 259–275.
Y. Colin de Verdière and B. Parisse, Equilibre instable en regime semi-classique, Comm. Part. Diff. Eqs. 19 (1994) 1535–1563.
Y. Colin de Verdière and B. Parisse, Equilibre instable en regime semi-classique II. Conditions de Bohr-Sommerfeld, Ann. Inst. H. Poincare 61 (1994) 347–367.
P. Collet, H. Epstein, and G. Gallavotti, Perturbations of geodesic flows on surfaces of constant negative curvature and their mixing properties, Comm. Math. Phys. 95 (1984) 61–112.
M. Combescure and D. Robert, Distribution of matrix elements and level spacings for classically chaotic systems, Ann. Inst. H. Poincare 61 (1994) 443–483.
A. Comtet, On the Landau levels on the hyperbolic plane, Ann. Phys. 173 (1987) 185–209.
A. Comtet and P. J. Houston, Effective action of the hyperbolic plane in a constant magnetic field, J. Math. Phys. 26 (1985) 185–191.
A. Comtet, B. Georgeot and S. Ouvry, Trace formula for Riemann surfaces with magnetic field, Phys. Rev. Lett. 71 (1993) 3786–3789.
A. Connes and M. A. Rieffel, Operator algebras in mathematical physics, Contemp. Math. 62 (1987).
J. Conrey and A. Ghosh, On the Selberg class of Dirichlet series, Duke Math. J. 72 (1993) 673–693.
J. H. Conway and N. J. A. Sloane, Sphere-packings, Lattices and Groups (Springer-Verlag, New York, 1988).
J. H. Conway and N. J. A. Sloane, Four-dimensional lattices with the same theta series, Duke Math. J. IMRN (1992) 93–96.
O. Costin and J. Lebowitz, Gaussian fluctuation in random matrices, Phys. Rev. Lett. 75 (1995) 69–72.
P. Cvitanovic et al., Classical and Quantum Chaos: A Cyclist Treatise, (preprint, 1996).
P. Cvitanovic and B. Eckhardt, Periodic orbit quantization of chaotic systems, Phys. Rev. Lett. 63 (1989) 823–826.
P. Cvitanovic, G. Vattay and A. Wirzba, Quantum fluids and classical determinants, (preprint, 1996).
E. Dahlberg and E. Trubowitz, A remark on two-dimensional periodic potentials, Comm. Math. Helv. 57 (1982) 130–134.
P. Dahlqvist, Approximate zeta functions for the Sinai billiard and related systems, Nonlin. 8 (1995) 11.
P. Dahlqvist, The Lyapunov exponent in the Sinai billiard in the small scatterer limit, (preprint, 1996).
I. Daubechies, Coherent states and projective representations of the linear canonical transformations, J. Math. Phys. 21 (1980) 1377–1389.
H. Davenport, Multiplicative Number Theory (Springer-Verlag, New York, 1980).
E. B. Davies, Heat Kernels and Spectral Theory (Cambridge University Press, Cambridge, 1989).
E. Davies, B. Simon and M. Taylor, L P spectral theory of Kleinian groups, J. Func. Anal. 78 (1988) 116–136.
S. De Bievre and M. Degli Esposti, Egorov theorems and equidistribution of eigenfunctions for the quantized sawtooth and baker maps, (preprint, 1996).
S. De Bievre, M. Degli Esposti and R. Giachetti, Quantization of a class of peicewise affine transformations on the torus, Comm. Math. Phys. 176 (1995) 73–94.
M. Degli Esposti, Quantization of the orientation preserving automorphisms of the torus, Ann. Inst. H. Poincare 58 (1993) 323–341.
M. Degli Esposti, Classical and quantum equidistribution: an (easy) example, (thesis, Pennsylvania State University, 1994).
M. Degli Esposti, S. Gräffi and S. Isola, Classical limit of the quantized hyperbolic toral automorphism, Comm. Math. Phys. 167 (1995) 471–507.
M. Degli Esposti, S. Gräffi and S. Isola, Equidistribution of periodic orbits: an overview of classical vs quantum results, Lect. Notes Math. 1589 (1994) 65–91.
M. Degli Esposti and S. Isola, Distribution of closed orbits for linear automorphisms of tori, Nonlin. 8 (1995) 827–842.
M. J. M. de Jong and C. W. J. Beenakker, Mesoscopic fluctuations in the shot-noise power of metals, Phys. Rev. B46 (1992) 13400–13406.
J. M. Deshouillers and H. Iwaniec, The non-vanishing of the Rankin-Selberg zeta-functions at special points, Contemp. Math. 53 (1986) 51–95.
J. M. Deshouillers, H. Iwaniec, R. Phillips, and P. Sarnak, Maass cusp forms, Proc. NAS 82 (1985) 3533–3534.
P. Deligne, La conjecture de Weil I, Publ. Math. IHES 48 (1974) 273–308.
P. Deligne, Cohomologie Etale, Lec. Notes Math. 569 (1977).
D. DeTurck, Audible and inaudible geometric properties, Rend. Sem. Fac. Sci. Cagliari 58 (1988) 1–26.
D. DeTurck and C. S. Gordon, Isospectral deformations I: Riemannian structures on two step nilspaces, Comm. Pure Appl. Math. 40 (1987) 367–387.
D. DeTurck and C. Gordon, Isospectral deformations II: trace formulas, metrics and potentials, Comm. Pure Appl. Math. 42 (1989) 1067–1095.
D. DeTurck, H. Gluck, C. Gordon, and D. Webb, You cannot hear the mass of a homology class, Comm. Math. Helv. 64 (1992) 589–617.
P. A. M. Dirac, Proc. Roy. Soc. London, A133 (1931) 60.
H. Donnelly, On the point spectrum for finite volume symmetric spaces of negative curvature, Comm. PDE 6 (1981) 963–982.
H. Donnelly, On the cuspidal spectrum for finite volume symmetric spaces, J. Diff. Geom. 17 (1982) 239–253.
O. N. Dorokhov, Pis’ma Zh. Eksp. Teor. Fiz. 36 (1982) 259
O. N. Dorokhov, JETP Lett 36 (1982) 318.
E. Doron, U. Smilansky and A. Prenkel, Experimental demonstration of chaotic scattering of microwaves, Phys. Rev. Lett. 65 (1990) 3072–3075.
T. Driscoll, Eigenmodes of isospectral drums, (preprint, 1995).
P. Duclos and H. Hogreve, On the semiclassical localization of the quantum probability, J. Math. Phys. 34 (1993) 1681–1691.
J. Duistermaat and V. Guillemin, Spectrum of elliptic operators and periodic bicharacteristics, Inv. math. 29 (1975) 39–79.
W. Duke, Hyperbolic distribution problems and half-integral weight Maass forms, Invent, math. 92 (1988) 73–90.
H. Dullin, P. Richter, and A. Wittek, A two-parameter study of the extent of chaos in a billiard system, (preprint, 1995).
G. V. Dunne, Hilbert space for charged particles in perpendicular magnetic fields, Ann. Phys. 215 (1992) 233–263.
G. V. Dunne, Slater decomposition of Laughlin states, Int. J. Mod. Phys. B7 (1993) 4783–4813.
F. J. Dyson, Statistical theory of the energy levels of complex systems, I, II, III, J. Math. Phys. 3 (1962) 140–175.
F. J. Dyson, A class of matrix ensembles J. Math. Phys. 13 (1972) 90–97.
F. J. Dyson and M. L. Mehta, Statistical theory of the energy levels of complex systems, IV, V, J. Math. Phys. 4 (1963) 701–719.
B. Eckhardt, Correlations in quantum time delay, Chaos 3 (1993) 613–617.
B. Eckhardt, Order and chaos in quantum irregular scattering: Wigner’s time delay, Vistas in Astronomy 37 (1993) 43–55.
B. Eckhardt, S. Fishman, K. Müller and D. Wintgen, Phys. Rev. A45 (1992) 3531.
B. Eckhardt, S. Fishman, J. Keating, O. Agam, J. Main, and K. Müller, Approach to ergodicity in quantum wave functions, Phys. Rev. E52 (1995) 5893.
B. Eckhardt and S. Grossmann, Phys. Rev. E50 (1994) 4571.
B. Eckhardt and J. Main, Semiclassical form-factor of matrix element fluctuations, Phys. Rev. Lett. 75 (1995) 2300–2303.
B. Eckhardt and G. Russberg, Resummation of classical and semiclassical periodic orbit formulas, Phys. Rev. E47 (1993) 1578–1588.
K. B. Efetov, Supersymmetry and the theory of disordered metals, Adv. Phys. 32 (1983) 53–127.
J. Elstrodt, Die resolvente zum eigenwertproblem der automorphen formen in der hyperbolischen ebene, Math. Ann. 203 (1973) 295–330
J. Elstrodt, Math. Zeit. 132 (1973) 99–134
J. Elstrodt, Math. Ann. 208 (1974) 99–132.
J. Elstrodt, F. Grunewald and J. Mennike, Discontinuous groups on three-dimensional hyperbolic space: analytical theory and arithmetic applications, Russ. Math. Sur. 38:1 (1983) 137–168.
J. Elstrodt, F. Grunewald and G. Mennicke, Elem. Anal. Theory of Numbers 17 (1985) 83.
M. Eisele and D. Mayer, Dynamical zeta functions for Artin’s billiard and the Venkov-Zograf factorization formula, (preprint, 1995).
C. Epstein, J. L. Hafner and P. Sarnak, Zeros of L-functions attached to Maass forms, Math. Z. 190 (1985) 113–128.
A. Feingold and A. Peres, Distribution of matrix elements of chaotic systems, Phys. Rev. A34 (1986) 591–595.
M. Fierz, Hel. Phys. Acta 17 (1944) 27.
K. Frahm, P. Brouwer, J. Meisen and C. Beenakker, Effect of the coupling to a superconductor on the level statistics of a metal grain in a magnetic field, (preprint, 1996).
A. Fujii, On the distribution of the zeros of the Riemann zeta function, Bull. AMS 81 (1975) 139–142.
A. Fujii, On the uniformity of the distribution of zeros of the Riemann zeta function, J. Reine Angew. Math. 302 (1978) 167–205.
P. Gallagher, Pair correlation of zeros of the zeta function, J. Math. 362 (19880 72–86.
P. Gallagher and J. Mueller, Primes and zeros in short intervals, J. reine Ang. Math. 303 (1978) 205–220.
G. Galperin, T. Krueger and S. Troubetzkoy, Local instability of orbits in polygonal and polyhedral billiards, Comm. Math. Phys. 169 (1995) 463–473.
G. Galperin, N. Chernov and A. Zemlyakov, Mathematics of Billiards (Cambridge University Press, Cambridge, 1995) 463–473.
G. Galperin, A. Stepin and Y. Vorobetz, Periodic billiard orbits in polygons, Russ. Math. Surv. 47 (1992) 5–80.
M. Gaudin, Reduction du probleme du billiard quantique triangulaire, J. de Phys. 48 (1987) 1633.
S. Gelbart and H. Jacquet, A relation between automorphic representations of GL Ann. Sci. Ecole Norm. Sup 11 (1978) 471–542.
S. Gelbart and I. Piatetski-Shapiro, On Shimura’s correspondence for modular forms of half integral weight, in Automorphic Forms, Representation Theory and Arithmetic (Springer-Verlag, Berlin, 1981).
B. Georgeot, Chaos, courbure negative et arithmetique (thesis, Universite de Paris-Sud, 1993).
C. Gérard, Asymptotique des poles de la matrice de scattering pour deux obstacles strictement convexes, Bull. Soc. Math. Fr. 116, no. 31 (1989).
C. Gérard and J. Sjöstrand, Semiclassical resonances generated by a closed trajectory of hyperbolic type, Comm. math. Phys. 108 (1987) 391–421.
C. Gérard and J. Sjöstrand, Resonances en limite semiclassique et exposants de Lyapunov, Comm. math. Phys. 116 (1988) 193–213.
P. Gerard and E. Leichtman, Ergodic properties of eigenfunctions for the Dirichlet problem, Duke Math. J. 71 (1993) 559–607.
A. Ghosh, On the Riemann zeta function-mean value theorems and the distribution of |S(t)|, J. Numb. Thy. 17 (1983) 93–102.
S. Girvin and R. Prange, The Quantum Hall Effect (Springer-Verlag, New York, 1990).
D. Goldfeld, Analytic and arithmetic theory of Poincaré series, Asterisque 61 (1979) 95–107.
D. Goldfeld, On convolutions of non-holomorphic Eisenstein series, Adv. in Math. 39 (1981) 240–256.
D. Goldston, On the pair correlation conjecture for zeros of the Riemann zeta function, J. reine ang. Math. 385 (1988) 24–40.
A. Good, Local analysis of Selberg’s trace formula, LNM 1040 (Springer Verlag, Berlin, 1983).
C. Gordon, The Laplace spectra versus the length spectra of Riemannian manifolds, in Nonlinear Problems in Geometry, Cont. Math. 51 (1986) 63–80.
C. Gordon, When your can’t hear the shape of a manifold, Math. Intell. 11 (1989) 39–47.
C. Gordon, Isospectral closed Riemannian manifolds which are not locally isometric, J. Diff. Geom. 37 (1993) 639–650.
C. Gordon and E. S. Wilson, Isospectral deformations of compact solvmanifolds, J. Diff. Geom. 19 (1984) 245–256.
C. Gordon and E. Wilson, The spectrum of the Laplacian on Riemannian Heisenberg manifolds, Michigan Math. J. 33 (1986) 253–271.
C. Gordon, D. Webb and S. Wolpert, Isospectral plane domains and surfaces via Riemannian orbifolds, Inv. Math. 110 (1993) 1–22.
C. Gordon, D. Webb, and S. Wolpert, One cannot hear the shape of a drum, Bull. AMS (1993) 134–138.
H. D. Gräf, H. L. Harney, H. Lengener, C. H. Lewenkopf, et al., Distribution of eigenmodes in a superconducting stadium billiard with chaotic dynamics, Phys. Rev. Lett. 69 (1992) 1296–1299.
S. Gräffi and A. Martinez, Ergodic properties of infinite harmonic crystals: an analytic approach, (preprint, 1995).
C. Grosche, The path integral on the Poincaré upper half-plane with a magnetic field and for the Morse potential, Ann. Phys. 187 (1988) 110–134.
C. Grosche, Energy-level statistics of an integrable billiard system in a rectangle in the hyperbolic plane, J. Phys. A25 (1992) 4573–4594.
C. Grosche, Path Integrals, Hyperbolic Spaces, and Selberg Trace Formulae Formulae (World Scientific, Singapore, 1996)
V. Guillemin and D. Kazhdan, Some inverse spectral results for negatively curved 2-manifolds, Top. 19 (1980) 153–180.
L. Guillope, Sur la distribution des longueurs des geodesique fermees d’une surface compacte a bord totalement geodesique, Duke Math. J. 53 (1986) 827–848.
L. Guillope, Fonctions zeta de Selberg et surfaces de geometrie finie, Ad. Studies Pure Math. 21 (1992) 33–70.
L. Guillopé and M. Zworski, Upper bounds on the number of resonances for non-compact Riemann surfaces, (preprint, 1994).
E. Gutkin, Billiard flows on almost integrable polyhedral surfaces, Erg. Thy. Dyn. Sys. 4 (1984) 569–584.
E. Gutkin, Billiards in polygons, Physica 19D (1986) 311–333.
E. Gutkin, Billiards in polygons: survey of recent results, J. Stat. Phys. 83 (1996) 7–26.
E. Gutkin and N. Haydn, Topological entropy of generalized polygon exchanges, Bull. AMS 32 (1995) 50–56.
E. Gutkin and C. Judge, Geometry and arithmetic of translation surfaces with applications to polygonal billiards, (preprint, 1996).
E. Gutkin and A. Katok, Caustics for inner and outer billiards, Comm. Math. Phys. 173 (1995) 101–133.
M. Gutzwiller, Stochastic behavior in quantum scattering, Physica 7D (1983) 341–355.
M. Gutzwiller, The geometry of quantum chaos, Physica Scripta T9 (1985) 184–l92.
M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer-Verlag, New York, 1990).
J. H. Hannay and M. V. Berry, Quantization of linear maps on a torus — Fresnel diffraction by a periodic grating, Physica D1 (1980) 267–291.
J. H. Hannay and A. M. Ozorio de Almeida, Periodic orbits and a correlation function for the semiclassical density of states, J. Phys. A17 (1984) 3429–3440.
J. H. Hannay, J. Keating and A. Ozorio de Almeida, Optical realization of the baker’s transformation, Nonlin. 7 (1994) 1327–1342.
G. H. Hardy, The average order of the arithmetical functors P(x) and A(x), Proc. Lond. Math. Soc. 15 (1916) 192–213.
G. H. Hardy and J. E. Littlewood, Acta Math. 44 (1923) 1–70.
N. Haydn, Gibbs functionals on subshifts, Comm. Math. Phys. 134 (1990) 217–236.
D. Heath-Brown, Gaps between primes and the pair correlation of zeros of the zeta function, Acta Arith. 41 (1982) 85–99.
D. R. Heath-Brown, The distribution and moments of the error term in the Dirichlet divisor problem, Acta Arith. 60 (1992) 389–415.
D. Hejhal, The Selberg trace formula and the Riemann zeta function, Duke Math. J. 43 (1976) 441–482.
D. Hejhal, The Selberg Trace Formula for PSL(2, R), Vol. I, LNM 548 (1976).
D. Hejhal, The Selberg trace formula for PSL(2, R), vol. 2, LNM 1001 (1981).
D. A. Hejhal, Eigenvalues of the Laplacian for PSL(2, Z): “some new results and computational techniques, in International Symposium in Memory of Hua Loo-Keng”, Vol. 1 (Springer, 1991) 59–102.
D. Hejhal, Eigenvalues of the Laplacian for Hecke triangle groups, Mem. AMS 469 (1992)
D. Hejhal, On the distribution of zeros of a certain class of Dirichlet series, Inter. Math. Res. Notes 4 (1992) 83–91.
D. A. Hejhal and S. Arno, On Fourier coefficients of Maass waveforms for PSL(2, Z), Math. Comp. 61 (1993) 245–267.
D. Hejhal and B. Rackner, On the topography of Mass wave forms for PSX(2, Z), Exp. Math. 1 (1992) 275–305.
B. Helffer, A. Martinez and E. Robert, Ergodicite et limite semiclassique, Comm. Math. Phys. 109 (1987) 313–326.
S. Helgason, Groups and Geometric analysis (Academic Press, New York, 1984).
E. Heller, Bound-state eigenfunctions of classically chaotic Hamiltonian systems: scars of periodic orbits, Phys. Rev. Lett. 53 (1984) 1515–1518.
E. Heller and S. Tomsovic, Postmodern quantum mechanics, Physics Today 7 (1993) 38–46.
M. Henon and J. Wisdom, The Benettin-Strelcyn oval billiard revisited, Physica 8D (1983) 157–169.
F. Henyey and N. Pomphrey, The autocorrelation function of a pseudointegrable system, Physica 6D (1982) 78–94.
A. Hobson, J. Math. Phys. 16 (1976) 2210–2214.
L. Hörmander, The spectral function of an elliptic operator, Acta Math. 121 (1968) 193–218.
H. Huber, Zur analytischen theorie hyperbolischer raumformen und bewegungsgruppen, I, II, Math. Ann. 138 (1959)1–26;
H. Huber, Zur analytischen theorie hyperbolischer raumformen und bewegungsgruppen, I, II, Math. Ann. 142 (1961) 385–398.
A. Hüffmann, Disordered wires from a geometric viewpoint, J. Phys. A23 (1990) 5733–5744.
M. Huxley, Scattering matrices for congruence subgroups, in Modular Forms (R. A. Rankin, ed., Ellis Horwood, 1984).
M. Huxley, Exponential sums and lattice points, Proc. Lond. Math. Soc. 60 (1990) 470–502.
M. Huxley, Exponential sums and lattice points, II, Proc. Lond. Math. Soc. 66 (1993) 279–301.
R. Iengo and D. Li, Quantum mechanics and quantum Hall effect on Riemann surfaces, preprint SISSA/ISAS/100/93.
S. Iida, H. A. Weidenmüller and J. A. Zuk, Wave propagation through disordered media and universal conductance, Phys. Rev. Lett. 64 (1990) 583–586.
S. Iida, H. A. Weidenmüller and J. A. Zuk, Statistical scattering theory, the supersymmetry method and universal conductance fluctuations, Ann. Phys. 200 (1990) 219–270.
M. Ikawa, On the poles of the scattering matrix for two convex obstacles, J. Math. Kyoto Univ. 23 (1983) 127–194;M. Ikawa, On the poles of the scattering matrix for two convex obstacles, J. Math. Kyoto Univ. 23 (1983) 795–802.
M. Ikawa, Precise information on the poles of the scattering matrix for two strictly convex obstacles, J. EDP St. Jean de Monts (1985).
A. Ikeda, Isospectral problem for spherical space forms, in Spectra of Riemannian Manifolds (ed., M. Berger et al., Kaigai Publications, 1983) 57–63.
Y. Imry, Europhys. Lett. 1 (1986) 249.
A. Ishibashi, D. Ravenhall, R. Schult and H. Wyld, Energy levels of charged particles confined in a multiply connected structure in a magnetic field, J. App. Phys. 73 (1993) 2364.
H. Iwaniec, Prime geodesic theorem, J. Reine Angew. Math. 349 (1984) 136–159.
H. Iwaniec, Fourier coefficients of modular forms of half-integral weight, Invent, math. 87 (1987) 385–401.
H. Iwaniec, Small eigenvalues of Laplacian for Γ0(N), Acta Arith. LVI (1990) 65–82.
H. Iwaniec and P. Sarnak, L ∞ norms of eigenfunctions of arithmetic surfaces, Ann. Math 141 (1995) 301–320.
D. Jakobson, Quantum unique ergodicity for Eisenstein series on PSL 2(Z)\PSL 2(R), Ann. Inst. Fourier, Grenoble 44 (1994) 1477–1504.
D. Jakobson, Quantum limits on flat tori, (preprint, 1995).
R. Jalabert and J-L Pichard, Quantum mesoscopic scattering: disordered systems and Dyson circular ensembles, CEA-Saclay S94/070.
R. A. Jalabert, J. L. Pichard, and C. W. J. Beenakker, Long-range energy level interaction in small metallic particles, Europhys. Lett. 24 (1993) 1–6.
R. A. Jalabert, J. L. Pichard and C. W. J. Beenakker, Universal quantum signatures of chaos in ballistic transport, Europhys. Lett. 27 (1994) 255–260.
R. A. Jalabert, A. D. Stone and Y. Alhassid, Statistical theory of coulomb blockade oscillations: quantum chaos in quantum dots, Phys. Rev. Lett. 68 (1992) 3468–3471.
D. Joyner, Distribution Theorems of L-Functions (Pitman, Boston, 1986).
D. Joyner, On the Montgomery-Dyson hypothesis, Proc. Amalfi Conf. Anal. Number Theory, (ed. E. Bombieri, et al., 1992) 331–369.
D. Joyner, A note on gaps between zeros of L-functions, (preprint, 1995).
C. Judge, (thesis, University of Maryland, 1993).
C. Judge, On the existence of Maass cusp forms on hyperbolic surfaces with cone points, J. AMS (to appear, 1994).
M. Kac, Can one hear the shape of a drum? Amer. Math. Monthly 73 (1966) 1–23.
D. Kashdan, Construction of Γ—rational groups, Func. Anal. Appl. 2 (1968).
A. Katok, The growth rate for the number of singular and periodic orbits for a polygonal billiard, Comm. Math. Phys. 111 (1987) 151–160.
A. Katok and B. Hasselblatt, Introduction of the Modern Theory of Dynamical Systems (Cambridge University Press, Cambridge, 1995).
A. Katok and J.-M. Strelcyn, Invariant manifolds, entropy and billiards; smooth maps with singularities, LNM 1222 (Springer, New York, 1986).
J. Keating, The semiclassical sum rule and Riemann’s zeta-function, in Quantum Chaos (ed. H. Cerdeira et al., World Scientific, Singapore, 1991) 280–294.
J. Keating, The cat maps: quantum mechanics and classical motion, Nonlin. 4 (1991) 309–341.
J. Keating, The Riemann zeta-function and quantum chaology, (preprint, 1991).
J. Keating, The quantum mechanics of chaotic systems or Can one hear the chaology of a drum? (preprint).
J. Keating, The Riemann zeta function and quantum chaology, in Quantum Chaos (ed., G. Casati et al., North-Holland, Amsterdam, 1993) 145–185.
J. Keating and M. Berry, J. Phys. A20 (1987) L1139.
J. Keating and M. Sieber, Proc. Roy. Soc. A447 (1994) 413.
D. G. Kendall, On the number of lattice points inside a random oval, Quart. J. Math. 19 (1948) 1–26.
S. Kerckhoff, S. Masur, and H. Smillie, Ergodicity of billiard flows and quadratic differentials, Ann. Math. 124 (1986) 293–311.
K. Khuri-Makdisi, Relations between Fourier coefficients of nonholomorphic Hilbert modular forms of half-integral weight and special values of Dirichlet series (thesis, Princeton University, 1993).
Y. Kitaoka, Positive definite quadratic forms with the same representation numbers, Arch. Math. 28 (1977) 495–497.
H. D. Kloosterman, The behaviour of general theta functions under the modular group and the characters of binary modular congruence groups I, Ann. Math. 47 (1946) 317.
A. Knauf, Ergodic and topological properties of coulombic periodic potentials, Comm. Math. Phys. 110 (1987) 89–112.
A. Knauf, Coulombic periodic potentials: the quantum case, Ann. Phys 191 (1989) 205–240.
M. Kneser, Lineare relationen zwischen darstellungszahlen quadratischer formen, Math. Ann. 168 (1967) 31–39.
W. Kohnen, Modular forms of half-integral weight on Γ0(4), Math. Ann. 248 (1980) 249–266.
W. Kohnen, Fourier coefficients of modular forms of half-integral weight, Math. Ann. 271 (1985) 237–268.
W. Kohnen, Newforms of half-integral weight, J. reine angew. Math. 32–72.
W. Kohnen and D. Zagier, Values of L-series of modular forms at the center of the critical strip, Invent, math. 64 (1981) 175–198.
D. Kosygin, A. Minasov and Y. Sinai, Statistical properties of the Laplace- Beltrami operator on Liouville surfaces, Usp. Mat. Nauk 48 (1993) 3–130.
S-Y. Koyama, Determinant expression of Selberg zeta functions, Trans. AMS 324 (1991) 149–168
S-Y. Koyama, Determinant expression of Selberg zeta functions, Trans. AMS 329 (1992) 755–772
S-Y. Koyama, Proc. AMS 113 (1991) 303–311.
V. Kozlov and D. Treshchev, Billiard — A Genetic Introduction to the Dynamics of Systems with Impacts (American Math. Society, Providence, 1991).
T. Kubota, Elementary Theory of Eisenstein Series, (Wiley, New York, 1973).
A. Kudrolli et al., Signatures of chaos in quantum billiards: microwave experiments, Phys. Rev. E49 (1994) R11–R14.
A. Kudrolli, V. Kidambi and S. Sridhar, Experimental studies of chaos and localization in quantum wavefunction, Phys. Rev. Lett. 75 (1995) 822–825.
A. Kudrolli and S. Sridhar, Microwave 2-disk scattering, (preprint, 1995).
A. Kudrolli and S. Sridhar, GOE in a microwave stadium billiard, Phys Rev. Lett. 76 (1996) 3036.
A. Kudrolli and S. Sridhar, Experiments on quantum chaos using microwav cavities: results for the psuedo-integrable L-billiard, (preprint, 1996).
M. Kus and K. Zyczkowski, Phys. Rev. A44 (1991) 956.
L. Landau, Z. Phys. 64 (1930) 629.
R. Langlands, Problems in the theory of automorphic forms, LNM 170 (1970) 18–61.
P. Lax and R. Phillips, The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces, J. Func. Anal. 46 (1982) 280–350.
P. Lax and R. Phillips, Scattering theory for automorphic functions, Ann. of Math. Studies (Princeton, 1976).
J. Leboeuf and A. Voros, Chaos revealing multiplicative representation of quantum eigenstates, J. Phys. A23 (1990) 1765–1773.
P. A. Lee and A. D. Stone, Universal conductance fluctuations in metals, Phys. Rev. Lett 55 (1985) 1622–1625.
P. A. Lee, A. D. Stone and H. Fukuyama, Universal conductance fluctuations in metals: effects of finite temperature, interactions and magnetic fields, Phys. Rev. B35 (1987) 1039–1070.
M. Lenci, Ergodic properties of the quantum ideal gas in the Maxwell-Boltzman statistics, (preprint, 1996).
C. H. Lewenkopf and H. A. Weidenmüller, Stochastic versus semiclassical approach to quantum chaotic scattering, Ann. Phys. 212 (1991) 53–83.
W. Li, Newforms and functional equations, Math. Ann. 212 (1975) 285–315.
G. Lion and M. Vergne, The Weil representation, Maslov index and Theta Series (Birkhauser, Boston, 1980).
W. Luo, On the nonvanishing of Rankin-Selberg L-functions, Duke Math. J. 69 (1993) 411–425.
W. Luo, Zeros of Hecke L-functions associated with cusp forms, Acta Arith. 71 (1995) 139–158.
W. Luo, Z. Rudnick, and P. Sarnak, On Selberg’s eigenvalue conjecture, Geom. Func. Anal. 5 (1995) 387–401.
W. Luo and P. Sarnak, Number variance for arithmetic hyperbolic surfaces, Comm. Math. Phys. 161 (1994) 419–432.
W. Luo and P. Sarnak, Quantum ergodicity of eigenfunctions on PSL 2(Z)\H 2, Publ. IHES (to appear).
S. McDonald and A. Kaufman, Spectrum and eigenfunctions for a Hamil-tonian with stochastic trajectories, Phys. Rev. Lett. 42 (1979) 1189–1191.
S. McDonald and A. Kaufmann, Wave chaos in the stadium: statistical properties of short-wave solutions of the Helmholtz equation, Phys. Rev. A37 (1988) 3067–3086.
H. Maass, Über eine neue art von nichtanalytischen automorphen funktionen und die bestimmung Dirichletscher reihen durch funktional-gleichungen, Math. Ann. 121 (1949) 141–182.
H. Maass, Uber die raumliche Verteilung der punkte in gittern mit indefiniter metrik, Math. Ann. 138 (1959) 287–315.
C. Maclachlan and W. Reid, Commensurability classes of arithmetic Kleinian groups and their Fuchsian subgroups, Math. Proc. Camb. Phil. Soc. 102 (1987) 251–257.
C. Maclachlan and W. Reid, The arithmetic structure of tetrahedral groups of hyperbolic isometries, Mathematika 36 (1989) 221–240.
W. Magnus, Non-Euclidian Tesselations and their Groups (Academic Press, New York, 1974).
E. Margulis, On some application of ergodic theory to the study of manifolds of negative curvature, Func. Anal. Appl. 3 (1969) 89–90.
R. Markarian, New ergodic billiards: exact results, Nonlin. 6 (1993) 819–841.
J. Marklof, On multiplicities in length spectra of arithmetic hyperbolic three-orbifolds, Nonlin. 9 (1996) 517.
E. Marshalek and J. da Providencia, Sum rules, random-phase- approximations and constraint self-consistent fields, Phys. Rev. C7 (1973) 2281–229
H. Masur, Closed trajectories for quadratic differentials with an applicatio to billiards, Duke. Math. J. 53 (1986) 307–314.
H. Masur, The growth rate for trajectories of a quadratic differential, Erg. Thy. Dyn. Sys. 10 (1990) 151–176.
C. Matthies and F. Steiner, Selberg’s zeta function and the quantization of chaos, Phys. Rev. A44 (1991) R7877–R7880.
M. L. Mehta, Random Matrices and the Statistical Theory of Energy Levels (Academic, New York, 1990).
P. A. Mello, Central limit theorems on groups, J. Math. Phys. 27 (1986) 2876–2891.
P. A. Mello and J. L Pichard, Maximum entropy approach to quantum electronic transport, Phys. Rev. B40 (1989) 5276–5278.
P. A. Mello and J. L. Pichard, J. Phys. I (Paris) 1 (1991) 493.
P. A. Mello, P. Pereyra and N. Kumar, Macroscopic approach to multichannel disordered conductors, Ann. Phys. 181 (1988) 290–317.
P. A. Mello and A. D. Stone, Maximum entropy model for quantum mechanical interference effects in metallic conductors, Phys. Rev. B44 (1991) 3559–3576.
V. I. Mel’nikov, Fiz. Tverd. Tela 23 (1981) 782.
J. Meisen, P. Brouwer, K. Frahm and C. Beenakker, Induced superconductivity distinguishes chaotic from integrable billiards, (preprint, 1996).
J. Meisen, P. Brouwer, K. Frahm and C. Beenakker, Superconductor-proximity effect in chaotic and integrable billiards, (preprint, 1996).
W. H. Miller, Adv. Chem. Phys. 25 (1974) 69.
W. H. Miller, J. Chem. Phys. 63 (1975) 996.
J. Milnor, Eigenvalues of the Laplace operator on certain manifolds, Proc. Nat. Acad. Sci. 51 (1964) 542.
J. Milnor, Curvatures of left invariant metrics on Lie groups, Adv. Math. 21 (1976) 293–329.
M. Min-Oo, Spectral rigidity for manifolds with negative curvature operator, Cont. Math. Nonlin Problems in Geom. 51 (1986) 99–103.
H. L. Montgomery, The pair correlation of zeros of the zeta function, in Analytic Number Theory (ed., H. G. Diamond) Proc. Symp. Pure Math. 24 (1973) 181–193.
H. L. Montgomery, Proc. Symp. Pure Math 38 (1976) 307–310.
C. Moreno, Explicit formulas in the theory of automorphic forms, LNM 626 (1977) 73–216.
G. D. Mostow, Strong rigidity of locally symmetric spaces, Ann. Math. Studies 78 (1973).
E. Mucciolo, R. Capaz, B. Altshuler, and J. Joannopoulos, Manifestation of quantum chaos in electronic band structures, (preprint, 1994).
W. Müller, Spectral theory for Riemannian manifolds with cusps and related trace formula, Math. Nach. III (1983) 197–288.
W. Müller, The point spectrum and spectral geometry for Riemannian manifolds with cusps, Math. Nach. 125 (1986) 243–257.
W. Müller, Spectral geometry and scattering theory for certain complete surfaces of finite volume, Inven. math. 109 (1992) 265–305.
M. Ram Murty, Selberg’s conjectures and Artin L—functions, Bull. AMS 31 (1994) 1–14
K. A. Muttalib, J. L. Pichard, and A. D. Stone, Random matrix theory and universal statistics for disordered quantum conductors, Phys. Rev. Lett. 59 (1987) 2475–2478.
K. Nakamura, Quantum Chaos (Cambridge University Press, Cambridge, 1993).
K. Nakamura and H. Ishio, J. Phys. Soc. Jap. 61 (1992) 3939.
K. Nakamura and H. Thomas, Phys. Rev. Lett. 61 (1988) 247.
S. Niwa, Modular forms of half-integral weight and the integral of certain theta functions, Nagoya Math. J. 56 (1974) 147–161.
H. Ninnemann, Gutzwiller’s octagon and the triangular group T*(2, 3, 8) as models for the quantization of chaotic systems by Selberg’s trace formula (thesis, 1994); Int. J. Mod. Phys. B9 (1995) 1647.
S. Niwa, On Shimura’s trace formula, Nagoya Math. J. 66 (1977) 183–202.
A. M. Odlyzko, On the distribution of spacings between zeros of the zeta function, Math. Comput. 48 (1987) 273–308.
A. M. Odlyzko, The 1020-th zero of the Riemann zeta function and 70 million of its neighbors, (preprint, 1989).
H. Okada, T. Hashizume and H. Hasegawa, Transport characterization of Schottky in-plane gate Al 0.2 GA 0.7 As/GaAs quantum wire transitors realized by in-situ electrochemical process, Jpn. J. Appl. Phys. 34 (1995) Pt. 1, No. 12B 6971–6976.
B. Osgood, R. Phillips and P. Sarnak, Extremals of determinants of Laplacians, J. Fun. Anal. 80 (1988); 148–211; 212–234;
B. Osgood, R. Phillips and P. Sarnak, Extremals of determinants of Laplacians, Ann. Math. 129 (1989) 293–362.
A. Pandey, Ann. Phys. 119 (1979) 170.
A. Pandey, O. Bohigas and M.-J. Giannoni, Level repulsion in teh spectrum of two-dimensional harmonic oscillators, J. Phys. A 22 (1989) 4083–4088.
W. Parry and M. Pollicott, An analogue of the prime number theorem for closed orbits of Axiom A flows, Ann. Math. 118 (1983) 573–591.
S. J. Patterson, The Laplacian operator on a Riemann surface, Compos. Math. 31 (1975) 83–107.
S. J. Patterson, The limit set of a Fuchsian group, Acta Math. 136 (1976) 241–273.
S. J. Patterson, Examples of Fuchsian groups, Proc. Lond. Math. Soc. 36 (1979) 276–298.
S. J. Patterson, On a lattice-point problem in hyperbolic space and related questions in spectral theory, Ark. f. matem. 26 (1988) 167–172.
N. Pavloff and C. Schmit, Diffractive orbits in quantum billiards, Phys. Rev. Lett. 75 (1995) 61–64.
P. Pechukas, Distribution of energy eigenvalues in the irregular spectrum, Phys. Rev. Let. 51 (1983) 943–946.
I. Percival and F. Vivaldi, Arithmetical properties of strongly chaotic motions, Physica D25 (1987) 105–130.
P. A. Perry, The Selberg zeta function and scattering poles for Kleinian groups, Bull. AMS 24 (1991) 327–333.
H. Pesce, Deformations isospectrales sur certaines nilvarietes et finitude spectrale des varietes de Heisenberg, Ann. Sci. Ecole Norm. Sup. 25 (1992) 515–538.
H. Pesce, Une formule de Poisson pour les varietes de Heisenberg, Duke Math. J. 73 (1994) 79–95.
Y. Pesin, Sov. Math. Dokl. 17 (1976) 196–199;
Y. Pesin, Russ. Math. Sur. 32 (1977), no. 4, 55–114.
H. Petersson, Zur analytischen théorie der grenzkreisgruppen, Math. Ann. 115 (1938) 23–67.
V. Petkov and L. Stoyanov, Geometry of Reflecting Rays and Inverse Spectra Problems, (Wiley, New York, 1992).
Y. Petridis, On the singular set, the resolvent and Fermi’s Golden Rule for finite volume hyperbolic surfaces, Manusc. math. 82 (1994) 331–347.
Y. Petridis, Spectral data for finite volume hyperbolic surfaces at the bottom ot the continuous spectrum, J. Func. Anal. 124 (1994) 61–94.
R. Phillips and P. Sarnak, On cusp forms for co-finite subgroups of the PSL 2(R), Invent. Math. 80 (1984) 339–364.
R. Phillips and P. Sarnak, The Weyl theorem and the deformation of discrete groups, Comm. Pure and Appl. Math. 38 (1985) 853–866.
R. Phillips and P. Sarnak, Spectrum of Fermat curves, Geom. Funct. Anal. 1 (1991) 79–146.
R. Phillips and P. Sarnak, Perturbation theory for the Laplacian on automorphic functions, J. Amer. Math. Soc. 5 (1992) 1–32.
R. Phillips and P. Sarnak, Automorphic spectrum and Fermi’s golden rule, J. d’anal. Math. 59 (1992) 179–187.
R. Phillips and P. Sarnak, Cusp forms for character varieties, Geom. Func. Anal. 4 (1994) 93–118.
J. Plemelj, Monat. Math. Phys 15 (1909) 93.
A. Pneuli, Scattering matrices and conductances of leaky tori, Ann. Phys. 231 (1994) 56–83.
A. Pneuli, Chern numbers and Hall conductances of Riemann surfaces, (preprint, 1994).
A. Pneuli, Adiabatic charge transport, the eta invariant and Hall conductance for spinors, (preprint, 1994a).
M. Pollicott, On the rate of mixing of Axiom A flows, Inv. Math. 81 (1985) 413–426.
G. Pólya, Heurestic reasoning in the theory of numbers, Amer. Math. Mon. 66 (1959) 375–384.
G. Pöschl and E. Teller, Bemerkungen zur Quantenmechanik des anharmonischen Oszillators, Z. Phys. 83 (1933) 143–151.
E. Pollak, A quasiclassical model for resonance widths in quantal colinear reactive scattering, J. Chem. Phys. 76 (1982) 5843–5848.
S. Prado, M. de Aguiar, J. Keating and R. de Carvalho, Semiclassical theory of magnetization for a two-dimensional non-interacting electron gas, J. Phys. A27 (1994) 6091–6106.
V. Prigodin, K. B. Efetov and S. Iida, Statistics of conductance fluctuations in quantum dots, Phys. Rev. Lett. 71 (1993) 1230–1233.
V. Prigodin, N. Taniguchi, A. Kudrolli, V. Kidambi and S. Sridhar, Spatial correlation in quantum chaotic systems with time-reversal symmetry: theory and experiment, (preprint, 1995).
H. Primak, H. Schanz, U. Smilansky and I. Ussishkin, Diffraction effects in the quantization of concave billiards, (preprint, 1996).
H. Primak and U. Smilansky, Quantization of the 3-dimensional Sinai billiard, Phys. Rev. Lett. 74 (1995) 4831–4834.
T. Prosen, Statistical properties of matrix elements in a Hamilton system between integrability and chaos, Ann. Phys. 235 (1994) 115–164.
T. Prosen, Numerical demonstration of the semiclassical matrix element probability distribution between integrability and chaos, J. Phys. A27 (1994) L569–L577.
T. Prosen and M. Robnik, Distribution and fluctuations of transition probabilities in a systems between integrability and chaos, J. Phys. A 26 (1993) L319–326.
T. Prosen and M. Robnik, Energy level statistics in the transition region between integrability and chaos, J. Phys. A26 (1993) 2371–2387.
T. Prosen and M. Robnik, Distribution and fluctuation properties of transition probabilities in a system between integrability and chaos, J. Phys. A26 (1993) L319–L326.
S. Rallis and G. Schiffman, Automorphic forms constructed from the Weil representation, holomorphic case, Amer. J. Math. 100 (1978) 1049–1122.
B. Randol, Small eigenvalues of the Laplace operator on compact Riemann surfaces, Bull. Amer. Math. Soc. 80 (1974) 996–1000.
B. Randol, The length spectrum of Riemann surface is always of unbounded multiplicity, Proc. AMS 78 (1980) 455.
M. Ratner, The central limit theorem for geodesic flows on n-dimensional manifolds of negative curvature, Israel J. Math. 16 (1973) 181–197.
M. Ratner, The rate of mixing for geodesic and horocycle flows, Ergod. Theo. Dynam. Sys. 7 (1987) 267–288.
D. Ravenhall, H. Wyld, and R. Schult, Quantum Hall effect at a four-terminal junction, Phys. Rev. Lett. 62 (1989) 1780–1783.
M. Reed and B. Simon, Methods of Modern Mathematical Physics 4 (Academic Press, New York, 1978).
P. Richens, Unphysical singularities in semiclassical level density expansions for polygon billiards, J. Phys. A16 (1983) 3961–3970.
P. Richens and M. Berry, Pseudointegrable systems in classical and quantum mechanics, Physica 2D (1981) 495–512.
J. M. Robbins and M. V. Berry, Discordance between quantum and classical correlation moments for chaotic system, J. Phys. A25 (1992) L961–965.
W. Rölcke, Das eigenwertproblem der automorphen formen in der hyperbolishen ebene, Math. Ann. 167 (1966) 292; 168 (1967) 261–324.
M. Robnik, Classical dynamics of a family of billiards with analytic boundaries, J. Phys. A16 (1983) 3971–3986.
M. Robnik, Quantising a generic family of billiards with analytic boundaries, J. Phys. A17 (1984) 1049–1074.
P. Rosenqvist, G. Vattay and A. Wirzba, Application of the diffraction trace formula to the three disk scattering system, J. Stat. Phys 83 (1996) 243–257.
P. Rosenqvist, N. Whelan and A. Wirzba, Small disks and semiclassical resonances, (preprint, 1996).
Z. Rudnick and P. Sarnak, The behavior of eigenstates of arithmetic hyperbolic manifolds, Comm. Math. Phys. 161 (1994) 195–213.
Z. Rudnick and P. Sarnak, Zeros of principal L-functions and random matrix theory, Duke Math. J. 81 (1996) 269–322.
D. Ruelle, Statistical Mechanics (Benjamin, New York, 1969).
D. Ruelle, Thermodynamic formalism (Addison-Wesley, Reading, 1978).
D. Ruelle, Locating resonances for Axiom A dynamical systems, J. Stat. Phys. 44 (1986) 281–292.
D. Ruelle, One dimensional Gibbs states and Axiom A diffeomorphisms, J. Diff. Geom. 25 (1987) 117–137.
H. H. Rugh, The correlation spectrum for hyperbolic analytic maps, Nonlinearity 5 (1992) 1237–1263.
H. H. Rugh, Generalized Fredholm determinants and Selberg zeta functions for Axiom A dynamical systems, (preprint, 1994).
R. Salem and A. Zygmund, Some properties of trigonometric series whose terms have random signs, Acta Math. 91 (1954) 245–301.
P. Sarnak, Class numbers of indefinite binary quadratic forms, J. Numb. Thy. 15 (1982) 229–247; 21 (1985) 333–346.
P. Sarnak, Additive number theory and Maass forms, LNM 1052 (1982) 286–309.
P. Sarnak, On cusp forms, Contemp. Math. 53 (1986) 393–407.
P. Sarnak, Determinants of Laplacians, Comm. Math. Phys. 110 (1987) 112–120.
P. Sarnak, Statistical properties of eigenvalues of the Hecke operators, (preprint, 1984).
P. Sarnak, On cusp forms II, in I. Piatetski-Shapiro’s Festschrift (1990) 237–251.
P. Sarnak, Some Applications of Modular Forms (Cambridge University Press, Cambridge, (1990).
P. Sarnak, Arithmetic Quantum Chaos, First Annual R. A. Blyth Lectures (1993); Isr. Math. Conf. Proc. 8 (1995) 183–256.
P. Sarnak, Spectra and eigenfunctions of Laplacians, (preprint, 1995).
P. Sarnak, Selberg’s eigenvalue conjecture, Notices AMS 42 (1995) 1272–1277.
C. Schmit, Triangular billiards on the hyperbolic plane: spectral properties, (preprint, 1991).
C. Schmit and C. Jacquemin, Classical quantization of a compact billiard on the pseudo-sphere, (preprint, 1991).
C. Schmit, Quantum and classical properties of some billiards on the hyperbolic plane, in Les Houches Lectures 52 (1991) 333–369.
A. Schnirelman, Ergodic properties of eigenfunctions, Usp. Math. Nauk 29 (1974) 181–182.
R. Schrader and M. Taylor, Semiclassical asymptotics, gauge fields and quantum chaos, J. Func. Anal. 83 (1989) 258–316.
R. Schubert, The trace formula and the distribution of eigenvalues of Schrödinger operators on manifolds all of whose geodesics are closed, (preprint, 1995).
R. Schult, D. Ravenhall and H. Wyld, Quantum bound states in a classically unbound system of crossed wires, Phys. Rev. B39 (1989) 5476–5479.
R. Schult, H. Wyld and D. Ravenhall, Quantum Hall effect and general narrow-wire circuits, Phys. Rev. B41 (1990) 12760.
P. Seba, Wave chaos in singular quantum billiard, Phys. Rev. Lett. 64 (1990) 1855–1858
A. Seeger and C. Sogge, Bounds for eigenfunctions of differential operators, Ind. J. Math. 38 (1989) 669–682.
A. Selberg, Contributions to the theory of the Riemann zeta-function, Arch. Math. Naturvid. B48 (1946) 89–155.
A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. 20 (1956) 47–87.
A. Selberg, On the estimation of Fourier coefficients of modular forms, in Proc. Sympos. Pure Math. 8 (1965) 1–15.
A. Selberg, Old and new conjectures and results about a class of Dirichlet series, in Proc. Amalfi Conf. on Anal. Number Theory (ed. E. Bombieri et al., 1989); in Collected Papers, Vol. 2 (Springer-Verlag, Berlin, 1991) 47–63.
T. Seligman, J. Verbaarschot and M. Zirnbauer, Phys. Rev. Lett. 53 (1985) 215;
T. Seligman, J. Verbaarschot and M. Zirnbauer, J. Phys. A18 (1985) 2751–2770.
F. Shahidi, Langlands’ functoriality conjecture, (preprint, 1989).
G. Shimura, On modular forms of half-integral weight, Ann. Math. 97 (1973) 440–481.
G. Shimura, On Fourier coefficients of Hilbert modular forms of half integral weight, Duke Math. J. 71 (1993) 502–557.
T. Shintani, On construction of holomorphic cusp forms of half-integral weight, Nagoya Math. J. 58 (1975) 83–126.
A. Shudo and Y. Shimizu, Extensive numerical study of spectral statistics for rational and irrational polygonal billiards, Phys. Rev. E47 (1993) 54–62.
A. Shushin and D. Wardlaw, Properties of time delay and S-matrix for chaotic scattering on a leaky surface of constant negative curvature, J. Phys. A25 (1992) 1503–1515.
M. Sieber, The hyperbola billiard: a model for the semiclassical quantization of chaotic systems (thesis, University of Hamburg, 1991).
M. Sieber, H. Primack, et al. Semiclassical quantization of billiards with mixed boundary conditions, J. Phys. A28 (1995) 5041–5078.
M. Sieber, U. Smilansky, S. Creagh and R. Littlejohn, Non-generic spectral statistics in the quantized stadium billiard, J. Phys. A16 (1993) 6217–6230.
M. Sieber and F. Steiner, Classical and quantum mechanics of a strongly chaotic billiard system, Physica D44 (1990) 248–266.
M. Sieber and F. Steiner, Generalized periodic-orbits sum rules for strongly chaotic systems, Phys. Lett. A144 (1990) 159–163.
M. Sieber and F. Steiner, Quantum chaos in the hyperbola billiard, Phys. Lett. A148 (1990) 415–420.
M. Sieber and F. Steiner, On the quantizaion of chaos, Phys. Rev. Lett. 67 (1991) 1941–1944.
B. Simon, Resonance in N-body quantum system, Ann. Math. 97 (1973) 247–274.
B. Simon, Nonclassical eigenvalue asymptotics, J. Fnal. Anal. 53 (1983) 84–98.
B. Simons and B. Altshuler, Phys. Rev. Lett. 70 (1993) 4063.
Ya. G. Sinai, The central limit theorem for geodesic flows on manifolds of constant negative curvature, Sov. Math. Dokl. 1 (1960) 983–987.
Ya. G. Sinai, Dynamical systems with elastic reflections, Ergodic properties of dispersing billiards, Russ. Math. Surv. 25 (1970) 137–191.
Ya. G. Sinai, Poisson distribution in a geometric problem, Adv. in Sov. Math. 3 (1991) 199–214.
Ya. G. Sinai, Mathematical problems in the theory of quantum chaos, LNM 1469 (1991) 41–59.
L. Sirko and P. Kock, Phys. Rev. E54 (1996) R21.
J. Sjöstrand and M. Zworski, Complex scaling and the distribution of scattering poles, J. AMS 4 (1991) 729–769.
J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles, I, Comm. Part. Diff. Eqs. 18 (1993) 847–857;
J. Sjöstrand and M. Zworski, Lower bounds on the number of scattering poles II, J. Fnal. Anal. 123 (1994) 336–367.
J. Sjöstrand and M. Zworski, Estimation of the number of scattering poles near the real axis for strictly convex obstacles, Ann. Inst. Four. 43 (1993) 769–790.
M. Skriganov, The spectrum band structure of the three-dimensional Schrödinger operator with periodic potential, Invent. Math. 80 (1985) 107–121.
K. Slevin, J. L. Pichard, and P. A. Mello, Europhys. Lett. 16 (1991) 649.
U. Smilansky, in Chaos and Quantum Physics, M. J. Giannoni et al. eds. (Elsevier, New York, 1990).
U. Smilansky et al., J. Phys. A26 (1993) 2617;
U. Smilansky et al., J. Phys. A27 (1994) 4439.
F. T. Smith, Phys. Rev. 118 (1960) 349.
F. Smithies, Duke Math. J. 8 (1941) 107.
S. Sridhar, Phys. Rev. Lett. 67 (1991) 785.
S. Sridhar and E. Heller, Physical and numerical experiments on the wave mechanics of classically chaotic systems, Phys. Rev. A46 (1992) R1728–R1731.
S. Sridhar and A. Kudrolli, Experiments on not “Chearing the shape” of drums, Phys. Rev. Lett. 72 (1994) 2175–2178.
G. Steil, Uber die eigenwerte des Laplace operators und de Hecke Operatoren fur SL(2, Z), (preprint, 1993).
J. Stein and H.-J. Stöckmann, Phys. Rev. Lett. 68 (1992) 2867.
F. Steiner, Quantum Chaos, in Universitat Hamburg 1994: Schlaglichter der Forschung zum 75. Jahrestag, (ed. R. Ansorge, Reimer, Hamburg, 1994) 543–564.
F. Steiner and P. Trillenberg, Refined asymptotic expansion of the heat kernel for quantum billiards in unbounded regions, J. Math. Phys. 31 (1990) 1670–1676.
H.-J. Stöckmann and J. Stein, “Quantum” chaos in billiards studied by microwave absorption, Phys. Rev. Lett. 64 (1990) 2215–2218.
A. D. Stone and H. Bruus, Universal fluctuations effects in chaotic quantum dots, Surf. Sci. 305 (1994) 490–494.
A. D. Stone, P. A. Mello, K. A. Muttalib, and J. L. Pichard, Random matrix theory and maximum entropy models for disordered conductors, in Mesoscopic Phenomena in Solids, ed. B. L. Al’tshuler et al. (North-Holland, Amsterdam, 1991).
M. Stone, Quantum Hall Effect (World Scientific, Singapore, 1992).
M. Stone, H. Wyld and R. Schult, Edge-waves in the quantum Hall effect and quantum dots, Phys. Rev. B45 (1992) 14156.
D. Sullivan, Related aspects of positivity: A—potential theory on manifolds, lowest eigenstates, Hausdorff geometry, renormalized Markoff processes… (preprint, 1983).
T. Sunada, Euclidean versus non-euclidean aspects in spectral geometry, Prog. Theo. Phys. Suppl. 116 (1994) 235–250.
A. Szafer and B. Altshuler, Phys. Rev. Lett. 70 (1993) 587–590.
D. Szasz, On the K-property of some planar hyperbolic billiards, Comm. Math. Phys. 145 (1992) 595–604.
K. Takeuchi, On some discrete subgroups of SL(2, R), J. Fac. Sci. Un. Tokyo 16 (1969) 97–100.
K. Takeuchi, A characterization of arithmetic Fuchsian groups, J. Math. Soc. Japan 27 (1975) 600–612.
K. Takeuchi, Arithmetic triangular groups, J. Math. Soc. Japan 29 (1977) 91–106.
A. Weil, On some exponential sums, Proc. Nat. Acad. Sci. USA 34 (1948) 204–207.
A. Weil, Algebras with involutions and classical groups, J. Indian Math. Soc. 24 (1960) 589–623.
C. Weisbuch and B. Vinter, Quantum Semiconductor Structures (Academic Press, New York, 1991).
N. Whelan, Geometric and diffractive orbits in the scattering from confocal hyperbolae, (preprint, 1994).
N. Whelan, Semiclassical quantisation using diffractive orbits, (preprint, 1995).
E. P. Wigner, Phys. Rev. 98 (1955) 145.
E. P. Wigner, Random matrices in physics, SIAM Review 9 (1967) 1–23.
M. Wilkinson, A semiclassical sum rule for matrix elements of classically chaotic systems, J. Phys. A20 (1987) 2415–2423.
H. C. Williams and J. Broere, A computational technique for evaluating L(1, χ) and the class number of a real quadratic field, Math. Comp. 30 (1976) 887–893.
A. Winkler, Cusp forms and Hecke groups, J. Reine Angew. Math. 386 (1988) 187–204.
A. Wirzba, Validity of the semiclassical period orbit approximation in the 2-and 3-disk problems, Chaos 2 (1992) 77–83.
E. Witt, Eine identitat zwischen modulformen zweiten grades, Abh. Sem. Univ. Hamburg 14 (1941) 323–337.
M. Wojtkowski, Principles for the design of billiards with nonvanishing Lyapunov exponents, Comm. Math. Phys. 105 (1986) 391–414.
S. Wolpert, Disappearance of cusp forms in special families, Ann. Math. 139 (1994) 239–291.
H. Wu, D. Sprung and J. Martorell, Numerical investigation of isospectral cavities built from triangles, Phys. Rev. E51 (1995) 703–708.
D. Zagier, Eisenstein series and the Selberg trace formula, in Automorphic Forms, Representation Theory and Arithmetic (Springer-Verlag, Berlin, 1981) 305–355.
D. Zagier, The Rankin-Selberg method for automorphic functions which are not of rapid decay, J. Fac. Sci., Univ. Tokyo, Sect. 1A, 28 (1981) 415–439.
N. Zanon and J. L. Pichard, J. Phys. (Paris) 49 (1988) 907.
S. Zelditch, Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke Math. J. 55 (1987) 919–941.
S. Zelditch, Selberg trace formulae, pseudodifferential operators and geodesic periods of automorphic forms, Duke Math. J. 56 (1988) 295–344.
K. Zyczkowski, Classical and quantum billiards: integrable, nonintegrable, and pseudo-integrable, Acta Phys. Polon. B23 (1992) 245–270.
A. Zygmund, On Fourier coefficients and transforms of two variables, Studia Math., T.L (1974) 189–201.
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Hurt, N.E. (1997). References. In: Quantum Chaos and Mesoscopic Systems. Mathematics and Its Applications, vol 397. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8792-1_15
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