Abstract
The static position correlation in a quantum Coulomb plasma near a wall is studied by means of a model where two quantum charges are embedded in a classical plasma at equilibrium. Three kinds of walls are considered: a wall without electrostatic properties, a dielectric, and an ideal conductor. At large separations y along the wall, the correlation exactly decays as 1/y 3, though no algebraic tail exists for classical charges near an ideal conductor. This tail originates from thermal statistical and purely quantum fluctuations of polarization clouds which are deformed by the geometric constraint due to the wall and by the charges induced by influence inside a wall with electrical properties. The coefficient of the 1/y 3 tail can be calculated explicitly in a weak-coupling and low-delocalization regime. Then classical, diffraction, and purely quantum contributions are disentangled.
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REFERENCES
D. C. Brydges and P. Federbush, Comm. Math. Phys 73:197 (1980).
A. Alastuey and Ph. A. Martin, J. Stat. Phys. 39:405 (1985).
A. Alastuey and Ph. A. Martin, Phys. Rev. A 40:6485 (1989).
F. Cornu, Phys. Rev. E 53:4595 (1996).
Ph. A. Martin, Rev. Mod. Phys. 60:1075 (1988).
B. Jancovici, J. Stat. Phys. 39:427 (1985).
F. Cornu, Phys. Rev. E 58:5322 (1998).
F. Cornu, Europhys. Lett. 37:591 (1997).
B. Simon, Functional Integration and Quantum Physics (Academic, New York, 1969).
B. Jancovici, J. Stat. Phys. 29:263 (1982).
E. Lieb and J. L. Lebowitz, Adv. Math. 9:316 (1972).
Ph. Choquard, P. Favre and Ch. Gruber, J. Stat. Phys. 23:405 (1980); H. Totsuji, J. Chem. Phys. 75:871 (1981).
B. Jancovici, J. Stat. Phys. 28:43 (1982).
A. S. Usenko and I. P. Yakimenko, Sov. Techn. Phys. Lett. 5:549 (1979).
I. M. Gel'fand and G. E. Shilov, Generalized Functions, Vol. 1 (Academic, New York, 1964).
F. Cornu, Phys. Rev. E 58:5293 (1998).
F. Cornu, Phys. Rev. E 53:4562 (1996).
Ch. Gruber, Ch. Lugrin and Ph. A. Martin, J. Stat. Phys. 22:193 (1980).
F. Cornu, Phys. Rev. Lett. 78:1464 (1997).
B. Jancovici, Physica A 101:324 (1980).
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Aqua, J.N., Cornu, F. Classical and Quantum Algebraic Screening in a Coulomb Plasma near a Wall: A Solvable Model. Journal of Statistical Physics 97, 173–207 (1999). https://doi.org/10.1023/A:1004667018492
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DOI: https://doi.org/10.1023/A:1004667018492