Abstract.
Nuclear matter and finite nuclei exhibit the property of superfluidity by forming Cooper pairs. We review the microscopic theories and methods that are being employed to understand the basic properties of superfluid nuclear systems, with emphasis on the spatially extended matter encountered in neutron stars, supernova envelopes, and nuclear collisions. Our survey of quantum many-body methods includes techniques that employ Green functions, correlated basis functions, and Monte Carlo sampling of quantum states. With respect to empirical realizations of nucleonic and hadronic superfluids, this review is focused on progress that has been made toward quantitative understanding of their properties at the level of microscopic theories of pairing, with emphasis on the condensates that exist under conditions prevailing in neutron-star interiors. These include singlet S-wave pairing of neutrons in the inner crust, and, in the quantum fluid interior, singlet-S proton pairing and triplet coupled P-F-wave neutron pairing. Additionally, calculations of weak-interaction rates in neutron-star superfluids within the Green function formalism are examined in detail. We close with a discussion of quantum vortex states in nuclear systems and their dynamics in neutron-star superfluid interiors.
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References
J. Bardeen, L.N. Cooper, J.R. Schrieffer, Phys. Rev. 108, 1175 (1957)
A. Bohr, B.R. Mottelson, D. Pines, Phys. Rev. 110, 936 (1958)
A.B. Migdal, Nucl. Phys. A 13, 655 (1959)
N.N. Bogoliubov, Sov. Phys. Doklady 3, 279 (1958)
L.N. Cooper, Phys. Rev. 104, 1189 (1956)
K.A. Al-Hassanieh, C.D. Batista, P. Sengupta, A.E. Feiguin, Phys. Rev. B 80, 115116 (2009)
M. Kagan, Modern trends in Superconductivity and Superfluidity, Lect. Notes Phys. (Springer, Netherlands, 2014)
M.Y. Kagan, V.A. Mitskan, M.M. Korovushkin, Phys. Usp. 58, 733 (2015) arXiv:1511.03781
A.B. Migdal, Nucl. Phys. A 30, 239 (1962)
A.I. Larkin, A.B. Migdal, Sov. Phys. JETP 17, 1146 (1964)
V.L. Ginzburg, D.A. Kirzhnits, Sov. Phys. JETP 20, 1346 (1965)
G. Baym, C. Pethick, D. Pines, Nature 224, 673 (1969)
A. Hewish, S.J. Bell, J.D.H. Pilkington, P.F. Scott, R.A. Collins, Nature 217, 709 (1968)
T. Gold, Nature 218, 731 (1968)
G. Baym, C. Pethick, D. Pines, M. Ruderman, Nature 224, 872 (1969)
R.C. Kennedy, Nucl. Phys. A 118, 189 (1968)
J.W. Clark, C.H. Yang, Lett. Nuovo Cimento 3, 272 (1970)
C.-H. Yang, J.W. Clark, Nucl. Phys. A 174, 49 (1971)
J.W. Clark, C.-H. Yang, Lett. Nuovo Cimento (1971-1985) 2, 379 (1971)
M. Hoffberg, A.E. Glassgold, R.W. Richardson, M. Ruderman, Phys. Rev. Lett. 24, 775 (1970)
T. Takatsuka, R. Tamagaki, Prog. Theor. Phys. 46, 114 (1971)
T. Takatsuka, Prog. Theor. Phys. 48, 1517 (1972)
N.-C. Chao, J.W. Clark, C.-H. Yang, Nucl. Phys. A 179, 320 (1972)
T. Takatsuka, Prog. Theor. Phys. 50, 1754 (1973)
V.A. Khodel, V.V. Khodel, J.W. Clark, Nucl. Phys. A 598, 390 (1996)
O. Elgarøy, M. Hjorth-Jensen, Phys. Rev. C 57, 1174 (1998) arXiv:nucl-th/9708026
J.M. Cordes, G.S. Downs, J. Krause-Polstorff, Astrophys. J. 330, 847 (1988)
R. Manchester, Pulsar glitches and their impact on neutron-star astrophysics, arXiv:1801.04332 (2018)
C.J. Pethick, Rev. Mod. Phys. 64, 1133 (1992)
D. Page, J.M. Lattimer, M. Prakash, A.W. Steiner, Pairing and superfluidity of nucleons in neutron stars, in Novel Superfluids, edited by K.H. Bennemann, J.B. Ketterson International Series of Monographs on Physics (Oxford University Press, Oxford, UK, 2013) p. 505
C. Schaab, F. Weber, M.K. Weigel, N.K. Glendenning, Nucl. Phys. A 605, 531 (1996) arXiv:astro-ph/9603142
D.G. Yakovlev, C.J. Pethick, Annu. Rev. Astron. Astrophys. 42, 169 (2004) arXiv:astro-ph/0402143
A. Sedrakian, Prog. Part. Nucl. Phys. 58, 168 (2007) arXiv:nucl-th/0601086
D.G. Yakovlev, A.D. Kaminker, O.Y. Gnedin, P. Haensel, Phys. Rep. 354, 1 (2001) arXiv:astro-ph/0012122
A. Schmitt, P. Shternin, Reaction rates and transport in neutron stars, arXiv:1711.06520
I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008) arXiv:0704.3011
A.J. Leggett, S. Zhang, The BEC-BCS crossover: Some history and some general observations, in The BCS-BEC Crossover and the Unitary Fermi Gas, edited by W. Zwerger, Lect. Notes Phys., Vol. 836 (Berlin Springer Verlag, 2012) p. 33
S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 80, 1215 (2008) arXiv:0706.3360
L. Pitaevskii, S. Stringari, Bose-Einstein Condensation (Oxford University Press, 2003)
C.J. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases, 2nd edition (Cambridge University Press, 2008)
N. Chamel, P. Haensel, Living Rev. Relativ. 11, 10 (2008) arXiv:0812.3955
A. Bulgac, Phys. Rev. C 65, 051305 (2002) arXiv:nucl-th/0108014
M. Bender, P.-H. Heenen, P.-G. Reinhard, Rev. Mod. Phys. 75, 121 (2003)
S. Goriely, N. Chamel, J.M. Pearson, Phys. Rev. C 88, 061302 (2013)
J. Dobaczewski, W. Nazarewicz, Nuclear pairing: Basic phenomena revisited, in Fifty Years of Nuclear BCS: Pairing in Finite Systems, edited by R.A. Broglia, V. Zelevinsky, (World Sci. Pub., Singapore, 2013) pp. 40--60
J.C. Pei, G.I. Fann, R.J. Harrison, W. Nazarewicz, Y. Shi, S. Thornton, Phys. Rev. C 90, 024317 (2014) arXiv:1407.3848
S. Goriely, N. Chamel, J.M. Pearson, J. Phys. Conf. Ser. 665, 012038 (2016)
S. Goriely, N. Chamel, J.M. Pearson, Phys. Rev. C 93, 034337 (2016)
K. Bennaceur, A. Idini, J. Dobaczewski, P. Dobaczewski, M. Kortelainen, F. Raimondi, J. Phys. G 44, 045106 (2017) arXiv:1611.09311
U. Lombardo, H.-J. Schulze, Superfluidity in neutron star matter, in Physics of Neutron Star Interiors, edited by D. Blaschke, N.K. Glendenning, A. Sedrakian, Vol. 578 (Springer Verlag, Berlin, 2001) p. 30
D.J. Dean, M. Hjorth-Jensen, Rev. Mod. Phys. 75, 607 (2003) arXiv:nucl-th/0210033
T. Takatsuka, R. Tamagaki, Prog. Theor. Phys. Suppl. 112, 27 (1993)
N.N. Bogoljubov, Nuovo Cimento 7, 794 (1958)
P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, New York, N.Y., 1980)
A. Abrikosov, Fundamentals of the Theory of Metals (North-Holland, Amsterdam, 1988)
E.M. Lifshitz, L.P. Pitaevskii, Statistical Physics: Part 2: Theory of Condensed State (Pergamon Press, Oxford, UK, 1980)
A. Abrikosov, L. Gor’kov, I. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, N.Y., 1963)
L.P. Gor’kov, T.K. Melik-Barkhudarov, Sov. Phys. JETP 13, 1018 (1961)
H.-J. Schulze, A. Polls, A. Ramos, Phys. Rev. C 63, 044310 (2001)
H.-H. Fan, E. Krotscheck, J.W. Clark, J. Low Temp. Phys. 189, 470 (2017) arXiv:1707.07268
H. Heiselberg, C.J. Pethick, H. Smith, L. Viverit, Phys. Rev. Lett. 85, 2418 (2000) arXiv:cond-mat/0004360
E.M. Lifshitz, L.P. Pitaevskii, Physical Kinetics (Pergamon Press, Oxford, UK, 1981)
R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Phys. Rev. C 51, 38 (1995) arXiv:nucl-th/9408016
M. Lacombe, B. Loiseau, J.M. Richard, R.V. Mau, J. Côté, P. Pirès et al., Phys. Rev. C 21, 861 (1980)
V.G.J. Stoks, R.A.M. Klomp, C.P.F. Terheggen, J.J. de Swart, Phys. Rev. C 49, 2950 (1994) arXiv:nucl-th/9406039
R. Machleidt, Phys. Rev. C 63, 024001 (2001) arXiv:nucl-th/0006014
M. Baldo, O. Elgarøy, L. Engvik, M. Hjorth-Jensen, H.-J. Schulze, Phys. Rev. C 58, 1921 (1998) arXiv:nucl-th/9806097
R. Machleidt, D.R. Entem, Phys. Rep. 503, 1 (2011) arXiv:1105.2919
A.D. Jackson, A. Lande, R.A. Smith, Phys. Rep. 86, 55 (1982)
A.D. Jackson, A. Lande, R.A. Smith, Phys. Rev. Lett. 54, 1469 (1985)
M. Baldo, U. Lombardo, P. Schuck, Phys. Rev. C 52, 975 (1995)
A. Sedrakian, J.W. Clark, Phys. Rev. C 73, 035803 (2006) arXiv:nucl-th/0511076
M. Stein, A. Sedrakian, X.-G. Huang, J.W. Clark, Phys. Rev. C 90, 065804 (2014) arXiv:1410.1053
S.L. Shapiro, S.A. Teukolsky, Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects (Wiley-Interscience, New York, N.Y., 1983)
N.K. Glendenning, Compact Stars: Nuclear Physics, Particle Physics, and General Relativity (Springer, New York, N.Y., 2000)
F. Weber, Pulsars as Astrophysical Laboratories for Nuclear and Particle Physics (Institute of Physics, Bristol, UK, 1999)
T. Alm, G. Röpke, A. Sedrakian, F. Weber, Nucl. Phys. A 604, 491 (1996)
N.K. Glendenning, J. Schaffner-Bielich, Phys. Rev. C 60, 025803 (1999) arXiv:astro-ph/9810290
D.K. Campbell, R.F. Dashen, J.T. Manassah, Phys. Rev. D 12, 979 (1975)
R.F. Sawyer, A. Soni, Astrophys. J. 216, 73 (1977)
G. Baym, E. Flowers, Nucl. Phys. A 222, 29 (1974)
G. Baym, C. Pethick, Annu. Rev. Nucl. Part. Sci. 25, 27 (1975)
A.R. Raduta, A. Sedrakian, F. Weber, Mon. Not. R. Astron. Soc. 475, 4347 (2018) arXiv:1712.00584
B.D. Serot, J.D. Walecka, Int. J. Mod. Phys. E 6, 515 (1997) arXiv:nucl-th/9701058
Jie Meng, Relativistic Density Functional for Nuclear Structure (World Scientific, Singapore, 2016)
R.A. Broglia, V. Zelevinsky, Fifty Years of Nuclear BCS: Pairing in Finite Systems (World Sci. Pub., Singapore, 2013)
G.F. Bertsch, Nuclear pairing: Basic phenomena revisited, in Fifty Years of Nuclear BCS: Pairing in Finite Systems, edited by R.A. Broglia, V. Zelevinsky, (World Sci. Pub., Singapore, 2013) pp. 26--39
S. Hilaire, J.-F. Berger, M. Girod, W. Satula, P. Schuck, Phys. Lett. B 531, 61 (2002)
W.H. Long, J. Meng, N.V. Giai, Relativistic Hartree-Fock-Bogoliubov theory: Ground states and excitations, in Relativistic Density Functional for Nuclear Structure, edited by J. Meng, Int. Rev. Nucl. Phys., Vol. 10 (World Sci. Pub., Singapore, 2016) pp. 143--169
J.J. Li, J. Margueron, W.H. Long, N. Van Giai, Phys. Rev. C 92, 014302 (2015) arXiv:1506.04507
W.H. Long, P. Ring, N.V. Giai, J. Meng, Phys. Rev. C 81, 024308 (2010) arXiv:0812.1103
H. Kucharek, P. Ring, Z. Phys. A 339, 23 (1991)
A. Bulgac, Y. Yu, Phys. Rev. Lett. 88, 042504 (2002) arXiv:nucl-th/0106062
E. Garrido, P. Sarriguren, E. Moya de Guerra, P. Schuck, Phys. Rev. C 60, 064312 (1999) arXiv:nucl-th/9909026
J. Margueron, H. Sagawa, K. Hagino, Phys. Rev. C 77, 054309 (2008) arXiv:0712.3644
W. Satuła, D.J. Dean, J. Gary, S. Mizutori, W. Nazarewicz, Phys. Lett. B 407, 103 (1997) arXiv:nucl-th/9702054
W.A. Friedman, G.F. Bertsch, Phys. Rev. C 76, 057301 (2007) arXiv:nucl-th/0702070
J.-P. Delaroche, M. Girod, J. Libert, H. Goutte, S. Hilaire, S. Péru et al., Phys. Rev. C 81, 014303 (2010) arXiv:0910.2940
N. Schunck, L.M. Robledo, Rep. Prog. Phys. 79, 116301 (2016) arXiv:1511.07517
A. Bulgac, P. Magierski, K.J. Roche, I. Stetcu, Phys. Rev. Lett. 116, 122504 (2016) arXiv:1511.00738
J. Sadhukhan, W. Nazarewicz, N. Schunck, Phys. Rev. C 93, 011304 (2016) arXiv:1510.08003
M. Greiner, C.A. Regal, D.S. Jin, Phys. Rev. Lett. 94, 070403 (2005) arXiv:cond-mat/0407381
M.W. Zwierlein, A. Schirotzek, C.H. Schunck, W. Ketterle, Science 311, 492 (2006) arXiv:cond-mat/0511197
C. Chin, R. Grimm, P. Julienne, E. Tiesinga, Rev. Mod. Phys. 82, 1225 (2010)
P. Nozières, S. Schmitt-Rink, J. Low Temp. Phys. 59, 195 (1985)
G.C. Strinati, P. Pieri, G. Röpke, P. Schuck, M. Urban, Phys. Rep. 738, 1 (2018)
C. Regal, D. Jin, Experimental Realization of the BCS-BEC Crossover with a Fermi Gas of Atoms, Advances In Atomic, Molecular, and Optical Physics, Vol. 54 (Academic Press, 2007) pp. 1--79
A.I. Larkin, Y.N. Ovchinnikov, Sov. Phys. JETP 20, 762 (1965)
P. Fulde, R.A. Ferrell, Phys. Rev. 135, 550 (1964)
I. Bloch, Phys. World 17, 25 (2004)
J.K. Chin, D.E. Miller, Y. Liu, C. Stan, W. Setiawan, C. Sanner et al., Nature 443, 961 (2006)
M. Schreiber, S.S. Hodgman, P. Bordia, H.P. Lüschen, M.H. Fischer, R. Vosk et al., Science 349, 842 (2015)
W. Zwerger, J. Opt. B 5, S9 (2003) arXiv:cond-mat/0211314
C.S. Chiu, G. Ji, A. Mazurenko, D. Greif, M. Greiner, Quantum state engineering of a Hubbard system with ultracold fermions, arXiv:1712.07114
M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, I. Bloch, Nature 415, 39 (2002)
T. Esslinger, Annu. Rev. Cond. Matter Phys. 1, 129 (2010) arXiv:1007.0012
D.G. Ravenhall, C.J. Pethick, J.R. Wilson, Phys. Rev. Lett. 50, 2066 (1983)
M. Hashimoto, H. Seki, M. Yamada, Prog. Theor. Phys. 71, 320 (1984)
C.P. Lorenz, D.G. Ravenhall, C.J. Pethick, Phys. Rev. Lett. 70, 379 (1993)
C.J. Pethick, D.G. Ravenhall, Annu. Rev. Nucl. Part. Sci. 45, 429 (1995)
B. Schuetrumpf, W. Nazarewicz, Phys. Rev. C 92, 045806 (2015) arXiv:1508.06611
A.S. Schneider, D.K. Berry, M.E. Caplan, C.J. Horowitz, Z. Lin, Phys. Rev. C 93, 065806 (2016) arXiv:1602.03215
F.J. Fattoyev, C.J. Horowitz, B. Schuetrumpf, Phys. Rev. C 95, 055804 (2017) arXiv:1703.01433
X.-C. Yao, H.-Z. Chen, Y.-P. Wu, X.-P. Liu, X.-Q. Wang, X. Jiang et al., Phys. Rev. Lett. 117, 145301 (2016) arXiv:1606.01717
M. Iskin, Phys. Rev. A 78, 021604 (2008) arXiv:0804.1035
M. Takahashi, T. Mizushima, K. Machida, M. Ichioka, J. Low Temp. Phys. 148, 423 (2007)
Y. Yu, A. Bulgac, Phys. Rev. Lett. 90, 161101 (2003) arXiv:nucl-th/0212072
H.J. Warringa, A. Sedrakian, Phys. Rev. A 84, 023609 (2011) arXiv:1105.3644
H.J. Warringa, Phys. Rev. A 86, 043615 (2012)
A. Bulgac, Y. Yu, Phys. Rev. Lett. 91, 190404 (2003) arXiv:cond-mat/0303235
A.L. Fetter, Rev. Mod. Phys. 81, 647 (2009)
N.R. Cooper, Adv. Phys. 57, 539 (2008) arXiv:0810.4398
N. Verhelst, J. Tempere, Vortex structures in ultra-cold atomic gases, in Vortex Dynamics and Optical Vortices, edited by H. Perez-de-Tejada, (INTECH, 2017) p. 1
A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, 1971)
G.D. Mahan, Many-Particle Physics, 2nd edition (Plenum, New York, N.Y., 1993)
Y. Nambu, Phys. Rev. 117, 648 (1960)
L.P. Gor’kov, Sov. Phys. JETP 9, 505 (1958)
A. Migdal, Theory of Finite Fermi Systems and Applications to Atomic Nuclei (John Wiley and Sons Inc, New York, N.Y., 1967)
M. Baldo, I. Bombaci, U. Lombardo, Phys. Lett. B 283, 8 (1992)
A. Sedrakian, T. Alm, U. Lombardo, Phys. Rev. C 55, R582 (1997)
O. Elgarøy, L. Engvik, M. Hjorth-Jensen, E. Osnes, Nucl. Phys. A 604, 466 (1996) arXiv:nucl-th/9602020
O. Elgarøy, L. Engvik, M. Hjorth-Jensen, E. Osnes, Nucl. Phys. A 607, 425 (1996) arXiv:nucl-th/9604032
O. Elgarøy, L. Engvik, M. Hjorth-Jensen, E. Osnes, Phys. Rev. Lett. 77, 1428 (1996) arXiv:nucl-th/9604041
R.K. Su, S.D. Yang, T.T.S. Kuo, Phys. Rev. C 35, 1539 (1987)
T.L. Ainsworth, J. Wambach, D. Pines, Phys. Lett. B 222, 173 (1989)
J. Wambach, T.L. Ainsworth, D. Pines, Nucl. Phys. A 555, 128 (1993)
H.-J. Schulze, J. Cugnon, A. Lejeune, M. Baldo, U. Lombardo, Phys. Lett. B 375, 1 (1996)
W.H. Dickhoff, Phys. Lett. B 210, 15 (1988)
M. Schmidt, G. Röpke, H. Schulz, Ann. Phys. (N.Y.) 202, 57 (1990)
T. Alm, B.L. Friman, G. Röpke, H. Schulz, Nucl. Phys. A 551, 45 (1993)
A. Sedrakian, G. Röpke, T. Alm, Nucl. Phys. A 594, 355 (1995)
H. Stein, A. Schnell, T. Alm, G. Röpke, Z. Phys. A 351, 295 (1995)
P. Bożek, Phys. Rev. C 65, 034327 (2002) arXiv:nucl-th/0107055
P. Bożek, Phys. Lett. B 551, 93 (2003) arXiv:nucl-th/0202045
P. Bożek, P. Czerski, Phys. Rev. C 66, 027301 (2002) arXiv:nucl-th/0204012
P. Bożek, Phys. Rev. C 62, 054316 (2000) arXiv:nucl-th/0003048
H. Müther, W.H. Dickhoff, Phys. Rev. C 72, 054313 (2005) arXiv:nucl-th/0508035
A. Sedrakian, Phys. Rev. C 68, 065805 (2003) arXiv:nucl-th/0302040
L.G. Cao, U. Lombardo, P. Schuck, Phys. Rev. C 74, 064301 (2006) arXiv:nucl-th/0608005
C. Shen, U. Lombardo, P. Schuck, Phys. Rev. C 71, 054301 (2005) arXiv:nucl-th/0503008
A. Sedrakian, U. Lombardo, Phys. Rev. Lett. 84, 602 (2000) arXiv:nucl-th/9907076
A. Schwenk, B. Friman, G.E. Brown, Nucl. Phys. A 713, 191 (2003) arXiv:nucl-th/0207004
A. Schwenk, B. Friman, Phys. Rev. Lett. 92, 082501 (2004) arXiv:nucl-th/0307089
F. Barranco, P.F. Bortignon, R.A. Broglia, G. Colò, P. Schuck, E. Vigezzi et al., Phys. Rev. C 72, 054314 (2005)
S.S. Pankratov, M. Baldo, E.E. Saperstein, Phys. Rev. C 91, 015802 (2015) arXiv:1409.7225
J.M. Dong, U. Lombardo, W. Zuo, Phys. Rev. C 87, 062801 (2013) arXiv:1304.0117
P. Papakonstantinou, J.W. Clark, J. Low Temp. Phys. 189, 361 (2017) arXiv:1705.10463
C. Drischler, T. Krüger, K. Hebeler, A. Schwenk, Phys. Rev. C 95, 024302 (2017) arXiv:1610.05213
P. Finelli, S. Maurizio, J.W. Holt, EPJ Web of Conferences 95, 04021 (2015) arXiv:1411.7504
S. Maurizio, J.W. Holt, P. Finelli, Phys. Rev. C 90, 044003 (2014) arXiv:1408.6281
S. Srinivas, S. Ramanan, Phys. Rev. C 94, 064303 (2016) arXiv:1606.09053
D. Ding, A. Rios, H. Dussan, W.H. Dickhoff, S.J. Witte, A. Carbone et al., Phys. Rev. C 94, 025802 (2016) arXiv:1601.01600
A. Rios, A. Polls, W.H. Dickhoff, J. Low Temp. Phys. 189, 234 (2017) arXiv:1707.04140
A. Sedrakian, J.W. Clark, Nuclear Superconductivity in Compact Stars: BCS Theory and Beyond, in Pairing in Fermionic Systems: Basic Concepts and Modern Applications, edited by A. Sedrakian, J.W. Clark, M. Alford (World Scientific Publishing Co, 2006) p. 135
M. Stein, X.-G. Huang, A. Sedrakian, J.W. Clark, Phys. Rev. C 86, 062801 (2012) arXiv:1208.0123
J.W. Clark, A. Sedrakian, M. Stein, X.-G. Huang, V.A. Khodel, V.R. Shaginyan et al., J. Phys. Conf. Ser. 702, 012012 (2016)
P. Nozières, Le Problème à N Corps (Dunod, Paris, France, 1963)
G. Baym, C. Pethick, Landau Fermi-Liquid Theory: Concepts and Applications (Wiley-VCH Verlag, Weinheim, Germany, 2004.)
A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems (McGraw Hill, New York, 1971)
J.W. Clark, C.-G. Källman, C.-H. Yang, D.A. Chakkalakal, Phys. Lett. A 61, 331 (1976)
S. Babu, G.E. Brown, Ann. Phys. (N.Y.) 78, 1 (1973)
S.-O. Bäckman, C.-G. Källman, O. Sjöberg, Phys. Lett. B 43, 263 (1973)
S.-O. Bäckman, G.E. Brown, J.A. Niskanen, Phys. Rep. 124, 1 (1985)
H.A. Bethe, Annu. Rev. Nucl. Part. Sci. 21, 93 (1971)
G.M. Eliashberg, Sov. Phys. JETP 11, 696 (1960)
V.M. Galitskii, Sov. Phys. JETP 7, 104 (1958)
K.A. Brueckner, J.L. Gammel, Phys. Rev. 109, 1023 (1958)
V.J. Emery, Nucl. Phys. A 12, 69 (1959)
V.J. Emery, Nucl. Phys. A 19, 154 (1960)
D.J. Thouless, Ann. Phys. (N.Y.) 10, 553 (1960)
T. Alm, G. Röpke, M. Schmidt, Z. Phys. A 337, 355 (1990)
G. Röpke, A. Schnell, P. Schuck, P. Nozières, Phys. Rev. Lett. 80, 3177 (1998) arXiv:cond-mat/9803325
O.A. Rubtsova, V.I. Kukulin, V.N. Pomerantsev, H. Müther, Phys. Rev. C 96, 034327 (2017) arXiv:1706.05299
F. Isaule, H.F. Arellano, A. Rios, Phys. Rev. C 94, 034004 (2016) arXiv:1602.05234
H.F. Arellano, F. Isaule, A. Rios, Eur. Phys. J. A 52, 299 (2016) arXiv:1606.04982
P. Danielewicz, Ann. Phys. 152, 239 (1984)
W. Botermans, R. Malfliet, Phys. Rep. 198, 115 (1990)
N.M. Hugenholtz, L. van Hove, Physica 24, 363 (1958)
L. Kadanoff, G. Baym, Quantum Statistical Mechanics: Green’s Function Methods in Equilibrium and Nonequilibrium Problems (W.A. Benjamin, 1962)
W.H. Dickhoff, D. van Neck, Many-Body Theory Exposed! Propagator Description of Quantum Mechanics in Many-Body Systems (World Scientific, Singapore, 2008)
T. Frick, H. Müther, Phys. Rev. C 68, 034310 (2003) arXiv:nucl-th/0306009
T. Frick, H. Müther, A. Polls, Phys. Rev. C 69, 054305 (2004) arXiv:nucl-th/0401015
A. Rios, A. Polls, A. Ramos, H. Müther, Phys. Rev. C 74, 054317 (2006) arXiv:nucl-th/0605080
A. Rios, A. Polls, I. Vidaña, Phys. Rev. C 79, 025802 (2009) arXiv:0809.1467
A. Carbone, A. Cipollone, C. Barbieri, A. Rios, A. Polls, Phys. Rev. C 88, 054326 (2013) arXiv:1310.3688
J.W. Clark, P. Westhaus, Phys. Rev. 141, 833 (1966)
E. Feenberg, Theory of Quantum Fluids (Academic Press, New York, N.Y., 1969)
J.W. Clark, L.R. Mead, E. Krotscheck, K.E. Kürten, M.L. Ristig, Nucl. Phys. A 328, 45 (1979)
J.W. Clark, Prog. Part. Nucl. Phys. 2, 89 (1979)
E. Krotscheck, J.W. Clark, Nucl. Phys. A 333, 77 (1980)
E. Krotscheck, R.A. Smith, A.D. Jackson, Phys. Rev. B 24, 6404 (1981)
E. Krotscheck, Theory of correlated basis functions, in Introduction to Modern Methods of Quantum Many-Body Theory and Their Applications, edited by A. Fabrocini, International Series of Monographs on Physics (World Sci. Pub., Singapore, 2002) pp. 265--328
S. Fantoni, Nucl. Phys. A 363, 381 (1981)
S. Fantoni, S. Rosati, Nuovo Cimento A 25, 593 (1975)
S. Fantoni, S. Rosati, Nuovo Cimento A 43, 413 (1978)
J.M.C. Chen, J.W. Clark, E. Krotscheck, R.A. Smith, Nucl. Phys. A 451, 509 (1986)
J.M.C. Chen, J.W. Clark, R.D. Davé, V.V. Khodel, Nucl. Phys. A 555, 59 (1993)
A. Fabrocini, S. Fantoni, A.Y. Illarionov, K.E. Schmidt, Nucl. Phys. A 803, 137 (2008) arXiv:0805.3491
A. Fabrocini, S. Fantoni, A.Y. Illarionov, K.E. Schmidt, Phys. Rev. Lett. 95, 192501 (2005) arXiv:nucl-th/0607034
G.E. Pavlou, E. Mavrommatis, C. Moustakidis, J.W. Clark, Eur. Phys. J. A 53, 76 (2017) arXiv:1612.02188
O. Benhar, G. De Rosi, J. Low Temp. Phys. 189, 250 (2017) arXiv:1705.06607
H.H. Fan, E. Krotscheck, T. Lichtenegger, D. Mateo, R.E. Zillich, Phys. Rev. A 92, 023640 (2015) arXiv:1409.5649
J.W. Clark, Cbf in bcs, in Fifty Years of Nuclear BCS: Pairing in Finite Systems, edited by R.A. Broglia, V. Zelevinsky (World Sci. Pub., Singapore, 2013) pp. 360--375
J.E. Mayer, M.G. Mayer, Statistical Mechanics (John Wiley & Sons, New York, N.Y., 1977)
E. Krotscheck, M.L. Ristig, Nucl. Phys. A 242, 389 (1975)
E. Krotscheck, J.W. Clark, Nucl. Phys. A 328, 73 (1979)
R.V. Reid Jr., Ann. Phys. (N.Y.) 50, 411 (1968)
B.D. Day, Phys. Rev. C 24, 1203 (1981)
S. Gandolfi, A.Y. Illarionov, K.E. Schmidt, F. Pederiva, S. Fantoni, Phys. Rev. C 79, 054005 (2009) arXiv:0903.2610
S. Gandolfi, A.Y. Illarionov, S. Fantoni, F. Pederiva, K.E. Schmidt, Phys. Rev. Lett. 101, 132501 (2008) arXiv:0805.2513
A. Gezerlis, J. Carlson, Phys. Rev. C 77, 032801 (2008) arXiv:0711.3006
S. Gandolfi, A.Y. Illarionov, F. Pederiva, K.E. Schmidt, S. Fantoni, Phys. Rev. C 80, 045802 (2009) arXiv:0907.1588
A. Gezerlis, J. Carlson, Phys. Rev. C 81, 025803 (2010) arXiv:0911.3907
S. Gandolfi, A. Gezerlis, J. Carlson, Annu. Rev. Nucl. Part. Sci. 65, 303 (2015) arXiv:1501.05675
V.R. Pandharipande, Nucl. Phys. A 178, 123 (1971)
A. Sedrakian, T.T.S. Kuo, H. Müther, P. Schuck, Phys. Lett. B 576, 68 (2003) arXiv:nucl-th/0308068
B.Y. Sun, W. Pan, Nucl. Phys. A 909, 8 (2013) arXiv:1304.6254
J. Kuckei, F. Montani, H. Müther, A. Sedrakian, Nucl. Phys. A 723, 32 (2003) arXiv:nucl-th/0210010
S. Ramanan, S.K. Bogner, R.J. Furnstahl, Nucl. Phys. A 797, 81 (2007) arXiv:0709.0534
N. Kaiser, T. Nikšić, D. Vretenar, Eur. Phys. J. A 25, 257 (2005) arXiv:nucl-th/0411038
A.M. Clogston, Phys. Rev. Lett. 9, 266 (1962)
B.S. Chandrasekhar, Appl. Phys. Lett. 1, 7 (1962)
G. Sarma, J. Phys. Chem. Solids 24, 1029 (1963)
A. Sedrakian, Phys. Rev. C 63, 025801 (2001) arXiv:nucl-th/0008052
S. Mao, X. Huang, P. Zhuang, Phys. Rev. C 79, 034304 (2009) arXiv:0812.0674
H. Müther, A. Sedrakian, Phys. Rev. Lett. 88, 252503 (2002) arXiv:cond-mat/0202409
H. Müther, A. Sedrakian, Phys. Rev. C 67, 015802 (2003) arXiv:nucl-th/0209061
P.F. Bedaque, H. Caldas, G. Rupak, Phys. Rev. Lett. 91, 247002 (2003) arXiv:cond-mat/0306694
H.T.C. Stoof, M. Houbiers, C.A. Sackett, R.G. Hulet, Phys. Rev. Lett. 76, 10 (1996) arXiv:cond-mat/9508079
R. Combescot, Europhys. Lett. 55, 150 (2001) arXiv:cond-mat/0007191
A. Sedrakian, J. Mur-Petit, A. Polls, H. Müther, Phys. Rev. A 72, 013613 (2005) arXiv:cond-mat/0504511
W.V. Liu, F. Wilczek, Phys. Rev. Lett. 90, 047002 (2003) arXiv:cond-mat/0208052
M.M. Forbes, E. Gubankova, W.V. Liu, F. Wilczek, Phys. Rev. Lett. 94, 017001 (2005) arXiv:hep-ph/0405059
A. Schmitt, Introduction to superfluidity -- Field-theoretical approach and applications, arXiv:1404.1284
G.B. Partridge, W. Li, R.I. Kamar, Y.-a. Liao, R.G. Hulet, Science 311, 503 (2006) arXiv:cond-mat/0511752
M.G. Alford, A. Schmitt, K. Rajagopal, T. Schäfer, Rev. Mod. Phys. 80, 1455 (2008) arXiv:0709.4635
R. Anglani, R. Casalbuoni, M. Ciminale, N. Ippolito, R. Gatto, M. Mannarelli et al., Rev. Mod. Phys. 86, 509 (2014) arXiv:1302.4264
K. Rajagopal, F. Wilczek, The condensed matter physics of QCD, in At the Frontier of Particle Physics: Handbook of QCD, edited by M. Shifman (World Sci. Pub., Singapore, 2001) pp. 2061--2151
R. Balian, H. Flocard, M. Veneroni, Temperature Dependence of Even-Odd Effects in Small Superconducting Systems, arXiv:cond-mat/9802006
J. Margueron, E. Khan, Phys. Rev. C 86, 065801 (2012) arXiv:1203.2134
A. Pastore, J. Margueron, P. Schuck, X. Viñas, Phys. Rev. C 88, 034314 (2013) arXiv:1303.5651
M. Belabbas, J.J. Li, J. Margueron, Phys. Rev. C 96, 024304 (2017) arXiv:1706.04222
A. Sedrakian, H. Müther, A. Polls, Phys. Rev. Lett. 97, 140404 (2006) arXiv:cond-mat/0605085
L. He, M. Jin, P. Zhuang, Phys. Rev. B 74, 214516 (2006) arXiv:cond-mat/0606322
M. Jin, L. He, P. Zhuang, Int. J. Mod. Phys. E 16, 2363 (2007)
J.J. Kinnunen, J.E. Baarsma, J.-P. Martikainen, P. Törmä, Rep. Prog. Phys. 81, 046401 (2018) arXiv:1706.07076
D.M. Eagles, Phys. Rev. 186, 456 (1969)
X.-G. Huang, Phys. Rev. C 81, 034007 (2010) arXiv:1002.0060
M. Jin, M. Urban, P. Schuck, Phys. Rev. C 82, 024911 (2010) arXiv:1005.1782
U. Lombardo, P. Nozières, P. Schuck, H.-J. Schulze, A. Sedrakian, Phys. Rev. C 64, 064314 (2001) arXiv:nucl-th/0109024
X.-l. Shang, W. Zuo, Phys. Rev. C 88, 025806 (2013) arXiv:1305.7456
M. Stein, A. Sedrakian, X.-G. Huang, J.W. Clark, G. Röpke, J. Phys. Conf. Ser. 496, 012008 (2014) arXiv:1401.4651
B. Cederwall, F.G. Moradi, T. Bäck, A. Johnson, J. Blomqvist, E. Clément et al., Nature 469, 68 (2011) arXiv:1101.2187
K. Sumiyoshi, G. Röpke, Phys. Rev. C 77, 055804 (2008) arXiv:0801.0110
S. Heckel, P.P. Schneider, A. Sedrakian, Phys. Rev. C 80, 015805 (2009) arXiv:0902.3539
M. Hempel, J. Schaffner-Bielich, Nucl. Phys. A 837, 210 (2010) arXiv:0911.4073
A.R. Raduta, F. Gulminelli, Phys. Rev. C 82, 065801 (2010) arXiv:1009.2226
M. Oertel, A.F. Fantina, J. Novak, Phys. Rev. C 85, 055806 (2012) arXiv:1202.2679
H. Pais, S. Chiacchiera, C. Providência, Phys. Rev. C 91, 055801 (2015) arXiv:1504.03964
F. Gulminelli, A.R. Raduta, Phys. Rev. C 92, 055803 (2015) arXiv:1504.04493
S. Typel, G. Röpke, T. Klähn, D. Blaschke, H.H. Wolter, Phys. Rev. C 81, 015803 (2010)
X.-H. Wu, S.-B. Wang, A. Sedrakian, G. Röpke, J. Low Temp. Phys. 189, 133 (2017) arXiv:1705.02525
M. Matsuo, Phys. Rev. C 73, 044309 (2006) arXiv:nucl-th/0512021
J. Margueron, H. Sagawa, K. Hagino, Phys. Rev. C 76, 064316 (2007) arXiv:0710.4241
A.A. Isayev, Phys. Rev. C 78, 014306 (2008) arXiv:0803.3362
Y. Kanada-En’yo, N. Hinohara, T. Suhara, P. Schuck, Phys. Rev. C 79, 054305 (2009) arXiv:0902.3717
T. Abe, R. Seki, Phys. Rev. C 79, 054002 (2009) arXiv:0708.2523
B.Y. Sun, H. Toki, J. Meng, Phys. Lett. B 683, 134 (2010) arXiv:0911.2559
S. Ramanan, M. Urban, Phys. Rev. C 88, 054315 (2013) arXiv:1308.0939
L. Salasnich, Phys. Rev. C 84, 067301 (2011) arXiv:1112.4004
T.T. Sun, B.Y. Sun, J. Meng, Phys. Rev. C 86, 014305 (2012) arXiv:1206.3407
M. Stein, A. Sedrakian, X.-G. Huang, J.W. Clark, Phys. Rev. C 93, 015802 (2016) arXiv:1510.06000
E. Gubankova, W.V. Liu, F. Wilczek, Phys. Rev. Lett. 91, 032001 (2003) arXiv:hep-ph/0304016
E. Gubankova, A. Schmitt, F. Wilczek, Phys. Rev. B 74, 064505 (2006) arXiv:cond-mat/0603603
R.M. Hornreich, J. Magn. & Magn. Mater. 15, 387 (1980)
C. Thompson, R.C. Duncan, Mon. Not. R. Astron. Soc. 275, 255 (1995)
R. Turolla, S. Zane, A.L. Watts, Rep. Prog. Phys. 78, 116901 (2015) arXiv:1507.02924
D. Chatterjee, T. Elghozi, J. Novak, M. Oertel, Mon. Not. R. Astron. Soc. 447, 3785 (2015) arXiv:1410.6332
M. Bocquet, S. Bonazzola, E. Gourgoulhon, J. Novak, Astron. Astrophys. 301, 757 (1995) arXiv:gr-qc/9503044
M. Sinha, A. Sedrakian, Phys. Rev. C 91, 035805 (2015) arXiv:1502.02979
A. Gezerlis, R. Sharma, Phys. Rev. C 85, 015806 (2012) arXiv:1111.0298
D. Blaschke, N. Chamel, Phases of dense matter in compact stars, arXiv:1803.01836
M. Oertel, M. Hempel, T. Klähn, S. Typel, Rev. Mod. Phys. 89, 015007 (2017) arXiv:1610.03361
J.M. Lattimer, M. Prakash, Science 304, 536 (2004) arXiv:astro-ph/0405262
J.M. Pearson, S. Goriely, N. Chamel, Phys. Rev. C 83, 065810 (2011)
F. Grill, J. Margueron, N. Sandulescu, Phys. Rev. C 84, 065801 (2011) arXiv:1107.4275
A. Pastore, M. Shelley, S. Baroni, C.A. Diget, J. Phys. G 44, 094003 (2017) arXiv:1707.08142
D.G. Ravenhall, C.J. Pethick, J.R. Wilson, Phys. Rev. Lett. 50, 2066 (1983)
K. Oyamatsu, M. Hashimoto, M. Yamada, Prog. Theor. Phys. 72, 373 (1984)
M. Hashimoto, H. Seki, M. Yamada, Prog. Theor. Phys. 71, 320 (1984)
C.P. Lorenz, D.G. Ravenhall, C.J. Pethick, Phys. Rev. Lett. 70, 379 (1993)
G. Watanabe, K. Iida, K. Sato, Nucl. Phys. A 676, 455 (2000) arXiv:astro-ph/0001273
W.G. Newton, J.R. Stone, Phys. Rev. C 79, 055801 (2009)
A.S. Schneider, C.J. Horowitz, J. Hughto, D.K. Berry, Phys. Rev. C 88, 065807 (2013) arXiv:1307.1678
C.J. Horowitz, D.K. Berry, C.M. Briggs, M.E. Caplan, A. Cumming, A.S. Schneider, Phys. Rev. Lett. 114, 031102 (2015) arXiv:1410.2197
F.J. Fattoyev, C.J. Horowitz, B. Schuetrumpf, Phys. Rev. C 95, 055804 (2017) arXiv:1703.01433
M.E. Caplan, A.S. Schneider, C.J. Horowitz, Phys. Rev. Lett. 121, 132701 (2018) arXiv:1807.02557
B. Schuetrumpf, K. Iida, J.A. Maruhn, P.G. Reinhard, Phys. Rev. C 90, 055802 (2014) arXiv:1407.4055
B. Schuetrumpf, M.A. Klatt, K. Iida, J.A. Maruhn, K. Mecke, P.G. Reinhard, J. Phys. Conf. Ser. 665, 012074 (2016)
B. Schuetrumpf, K. Iida, J.A. Maruhn, P.G. Reinhard, Phys. Rev. C 90, 055802 (2014) arXiv:1407.4055
C.J. Pethick, A.Y. Potekhin, Phys. Lett. B 427, 7 (1998) arXiv:astro-ph/9803154
D. Kobyakov, C.J. Pethick, Phys. Rev. Lett. 112, 112504 (2014) arXiv:1309.1891
M.E. Caplan, C.J. Horowitz, Rev. Mod. Phys. 89, 041002 (2017) arXiv:1606.03646
B. Haskell, A. Sedrakian, Superfluidity and Superconductivity in Neutron Stars, arXiv:1709.10340
T. Takatsuka, R. Tamagaki, Prog. Theor. Phys. 65, 1333 (1981)
M. Baldo, H.-J. Schulze, Phys. Rev. C 75, 025802 (2007)
M. Baldo, J. Cugnon, A. Lejeune, U. Lombardo, Nucl. Phys. A 536, 349 (1992)
G. Colucci, A. Sedrakian, Phys. Rev. C 87, 055806 (2013) arXiv:1302.6925
J.W. Negele, D. Vautherin, Nucl. Phys. A 207, 298 (1973)
A. Bulgac, Y. Yu, Int. J. Mod. Phys. E 13, 147 (2004) arXiv:nucl-th/0310066
S.A. Fayans, S.V. Tolokonnikov, E.L. Trykov, D. Zawischa, Nucl. Phys. A 676, 49 (2000) arXiv:nucl-th/0101012
M. Baldo, E.E. Saperstein, S.V. Tolokonnikov, Eur. Phys. J. A 32, 97 (2007) arXiv:nucl-th/0609031
X. Viñas, P. Schuck, M. Farine, J. Phys. Conf. Ser. 321, 012024 (2011)
P. Schuck, X. Viñas, Phys. Rev. Lett. 107, 205301 (2011)
J.M. Pearson, N. Chamel, A. Pastore, S. Goriely, Phys. Rev. C 91, 018801 (2015)
A.L. Goodman, Nucl. Phys. A 352, 30 (1981)
N. Sandulescu, Phys. Rev. C 70, 025801 (2004)
N. Sandulescu, N. van Giai, R.J. Liotta, Phys. Rev. C 69, 045802 (2004) arXiv:nucl-th/0402032
J. Margueron, M. Fortin, F. Grill, D. Page, N. Sandulescu, J. Phys. Conf. Ser. 321, 012031 (2011)
A. Pastore, Phys. Rev. C 91, 015809 (2015) arXiv:1412.8410
C. Monrozeau, J. Margueron, N. Sandulescu, Phys. Rev. C 75, 065807 (2007) arXiv:nucl-th/0703064
A. Pastore, N. Chamel, J. Margueron, Mon. Not. R. Astron. Soc. 448, 1887 (2015) arXiv:1501.03364
N. Chamel, S. Goriely, J.M. Pearson, M. Onsi, Phys. Rev. C 81, 045804 (2010) arXiv:1002.3705
M.V. Zverev, J.W. Clark, V.A. Khodel, Nucl. Phys. A 720, 20 (2003) arXiv:nucl-th/0301028
V.A. Khodel, J.W. Clark, M. Takano, M.V. Zverev, Phys. Rev. Lett. 93, 151101 (2004) arXiv:astro-ph/0402514
V.A. Khodel, J.W. Clark, M.V. Zverev, Phys. Rev. Lett. 87, 031103 (2001) arXiv:nucl-th/0101045
V.V. Khodel, V.A. Khodel, J.W. Clark, Nucl. Phys. A 679, 827 (2001) arXiv:nucl-th/0001006
B.S. Pudliner, V.R. Pandharipande, J. Carlson, S.C. Pieper, R.B. Wiringa, Phys. Rev. C 56, 1720 (1997) arXiv:nucl-th/9705009
W. Zuo, C.X. Cui, U. Lombardo, H.-J. Schulze, Phys. Rev. C 78, 015805 (2008)
X.R. Zhou, G.F. Burgio, U. Lombardo, H.-J. Schulze, W. Zuo, Phys. Rev. C 69, 018801 (2004)
S. Balberg, N. Barnea, Phys. Rev. C 57, 409 (1998) arXiv:nucl-th/9709013
T. Takatsuka, S. Nishizaki, Y. Yamamoto, R. Tamagaki, Prog. Theor. Phys. Suppl. 146, 279 (2002)
T. Takatsuka, S. Nishizaki, Y. Yamamoto, R. Tamagaki, Prog. Theor. Phys. 115, 355 (2006) arXiv:nucl-th/0601043
I. Vidaña, L. Tolós, Phys. Rev. C 70, 028802 (2004) arXiv:nucl-th/0405010
Y.N. Wang, H. Shen, Phys. Rev. C 81, 025801 (2010) arXiv:1002.0204
R. Xu, C. Wu, Z. Ren, Int. J. Mod. Phys. E 23, 1450078 (2014) arXiv:1409.7763
T. Takatsuka, S. Nishizaki, Y. Yamamoto, R. Tamagaki, Prog. Theor. Phys. 105, 179 (2001)
X.-R. Zhou, H.-J. Schulze, F. Pan, J.P. Draayer, Phys. Rev. Lett. 95, 051101 (2005)
S. Balberg, A. Gal, Nucl. Phys. A 625, 435 (1997) arXiv:nucl-th/9704013
M. Baldo, G.F. Burgio, H.-J. Schulze, Phys. Rev. C 61, 055801 (2000) arXiv:nucl-th/9912066
G.F. Burgio, H.-J. Schulze, A. Li, Phys. Rev. C 83, 025804 (2011) arXiv:1101.0726
T.A. Rijken, H.-J. Schulze, Eur. Phys. J. A 52, 21 (2016)
D. Chatterjee, I. Vidaña, Eur. Phys. J. A 52, 29 (2016) arXiv:1510.06306
T.A. Rijken, Nucl. Phys. A 691, 322 (2001)
I. Filikhin, A. Gal, Nucl. Phys. A 707, 491 (2002)
H. Garcilazo, A. Valcarce, J. Vijande, Phys. Rev. C 94, 024002 (2016) arXiv:1608.05192
T.A. Rijken, M.M. Nagels, Y. Yamamoto, Few Body Syst. 54, 801 (2013)
M. Fortin, C. Providência, A.R. Raduta, F. Gulminelli, J.L. Zdunik, P. Haensel et al., Phys. Rev. C 94, 035804 (2016)
M.E. Gusakov, P. Haensel, E.M. Kantor, Mon. Not. R. Astron. Soc. 439, 318 (2014)
W. Spinella, A systematic investigation of exotic matter in neutron stars, PhD Thesis (Claremont Graduate University/San Diego State University, 2017)
N. González-Jiménez, C. Petrovich, A. Reisenegger, Mon. Not. R. Astron. Soc. 447, 2073 (2015) arXiv:1411.6500
C. Schaab, A. Sedrakian, F. Weber, M.K. Weigel, Astron. Astrophys. 346, 465 (1999) arXiv:astro-ph/9904127
J. Boguta, Phys. Lett. B 106, 255 (1981)
J.M. Lattimer, M. Prakash, C.J. Pethick, P. Haensel, Phys. Rev. Lett. 66, 2701 (1991)
P.S. Shternin, M. Baldo, P. Haensel, Phys. Lett. B 786, 28 (2018) arXiv:1807.06569
A.D. Kaminker, C.J. Pethick, A.Y. Potekhin, V. Thorsson, D.G. Yakovlev, Astron. Astrophys. 343, 1009 (1999) arXiv:astro-ph/9812447
M. Prakash, M. Prakash, J.M. Lattimer, C.J. Pethick, Astrophys. J. Lett. 390, L77 (1992)
A.B. Migdal, E.E. Saperstein, M.A. Troitsky, D.N. Voskresensky, Phys. Rep. 192, 179 (1990)
T. Tatsumi, Prog. Theor. Phys. Suppl. 120, 111 (2013)
T. Muto, M. Yasuhira, T. Tatsumi, N. Iwamoto, Phys. Rev. D 67, 103002 (2003) arXiv:nucl-th/0301045
E. Flowers, M. Ruderman, P. Sutherland, Astrophys. J. 205, 541 (1976)
A.D. Kaminker, P. Haensel, D.G. Yakovlev, Astron. Astrophys. 345, L14 (1999) arXiv:astro-ph/9904166
D.N. Voskresensky, A.V. Senatorov, Sov. J. Nucl. Phys. 45, 657 (1987)
L.B. Leinson, A. Pérez, Phys. Lett. B 638, 114 (2006) arXiv:astro-ph/0606651
A. Sedrakian, H. Müther, P. Schuck, Phys. Rev. C 76, 055805 (2007) arXiv:astro-ph/0611676
E.E. Kolomeitsev, D.N. Voskresensky, Phys. Rev. C 77, 065808 (2008) arXiv:0802.1404
E.E. Kolomeitsev, D.N. Voskresensky, Phys. Rev. C 81, 065801 (2010) arXiv:1003.2741
A.W. Steiner, S. Reddy, Phys. Rev. C 79, 015802 (2009) arXiv:0804.0593
A. Sedrakian, Phys. Rev. C 86, 025803 (2012) arXiv:1201.1394
D. Page, J.M. Lattimer, M. Prakash, A.W. Steiner, Astrophys. J. 707, 1131 (2009) arXiv:0906.1621
C. Schaab, D. Voskresensky, A.D. Sedrakian, F. Weber, M.K. Weigel, Astron. Astrophys. 321, 591 (1997) arXiv:astro-ph/9605188
A. Sedrakian, A.E.L. Dieperink, Phys. Rev. D 62, 083002 (2000) arXiv:astro-ph/0002228
P.W. Anderson, Phys. Rev. 112, 1900 (1958)
N.N. Bogolyubov, V.V. Tolmachev, D.V. Shirkov, Fortsch. Phys. 6, 605 (1958)
A.J. Leggett, Phys. Rev. 147, 119 (1966)
D.G. Yakovlev, A.D. Kaminker, K.P. Levenfish, Astron. Astrophys. 343, 650 (1999) arXiv:astro-ph/9812366
L.B. Leinson, Phys. Rev. C 87, 025501 (2013) arXiv:1301.5439
P. Jaikumar, M. Prakash, Phys. Lett. B 516, 345 (2001) arXiv:astro-ph/0105225
M.J. Savage, J. Walden, Phys. Rev. D 55, 5376 (1997) arXiv:hep-ph/9611210
J. Keller, A. Sedrakian, Phys. Rev. C 87, 045804 (2013) arXiv:1205.6902
E.E. Kolomeitsev, D.N. Voskresensky, Phys. Rev. C 84, 068801 (2011) arXiv:1108.5899
N. Martin, M. Urban, Phys. Rev. C 90, 065805 (2014) arXiv:1406.0335
A.D. Sedrakian, Astrophys. Space sci. 236, 267 (1996)
V. Cirigliano, S. Reddy, R. Sharma, Phys. Rev. C 84, 045809 (2011) arXiv:1102.5379
N. Chamel, D. Page, S. Reddy, Phys. Rev. C 87, 035803 (2013) arXiv:1210.5169
M. Urban, M. Oertel, Int. J. Mod. Phys. E 24, 1541006 (2015) arXiv:1506.00483
S. Baroni, A. Pastore, F. Raimondi, F. Barranco, R.A. Broglia, E. Vigezzi, Phys. Rev. C 82, 015807 (2010)
M. Grasso, E. Khan, J. Margueron, N. Van Giai, Nucl. Phys. A 807, 1 (2008)
E. Khan, N. Sandulescu, N.V. Giai, Phys. Rev. C 71, 042801 (2005)
T. Inakura, M. Matsuo, Phys. Rev. C 96, 025806 (2017) arXiv:1707.05203
B. Carter, E. Chachoua, N. Chamel, Gen. Relativ. Gravit. 38, 83 (2006) arXiv:gr-qc/0507006
N. Chamel, Phys. Rev. C 85, 035801 (2012)
N. Chamel, Phys. Rev. Lett. 110, 011101 (2013) arXiv:1210.8177
N. Chamel, J. Low Temp. Phys. 189, 328 (2017) arXiv:1707.07854
G. Watanabe, C.J. Pethick, Phys. Rev. Lett. 119, 062701 (2017) arXiv:1704.08859
N. Martin, M. Urban, Phys. Rev. C 94, 065801 (2016) arXiv:1606.01126
C.J. Pethick, N. Chamel, S. Reddy, Prog. Theor. Phys. Suppl. 186, 9 (2010) arXiv:1009.2303
D. Kobyakov, C.J. Pethick, Phys. Rev. C 87, 055803 (2013) arXiv:1303.1315
A.F. Andreev, E.P. Bashkin, Sov. Phys. JETP 42, 164 (1976)
G.A. Vardanyan, D.M. Sedrakyan, Sov. Phys. JETP 54, 919 (1981)
M.A. Alpar, D. Pines, P.W. Anderson, J. Shaham, Astrophys. J. 276, 325 (1984)
D.M. Sedrakyan, K.M. Shakhabasyan, Astrophysics 16, 417 (1980)
R.I. Epstein, Astrophys. J. 333, 880 (1988)
P. Magierski, A. Bulgac, Nucl. Phys. A 738, 143 (2004)
N. Andersson, K. Glampedakis, W.C.G. Ho, C.M. Espinoza, Phys. Rev. Lett. 109, 241103 (2012) arXiv:1207.0633
M. Baldo, C. Ducoin, Phys. Rev. C 79, 035801 (2009) arXiv:0811.0604
M. Baldo, C. Ducoin, Phys. Rev. C 96, 025811 (2017) arXiv:1708.03794
P.F. Bedaque, A.N. Nicholson, S. Sen, Phys. Rev. C 92, 035809 (2015) arXiv:1408.5145
P.F. Bedaque, A.N. Nicholson, Phys. Rev. C 87, 055807 (2013) arXiv:1212.1122
P.F. Bedaque, S. Reddy, Phys. Lett. B 735, 340 (2014) arXiv:1307.8183
P.F. Bedaque, G. Rupak, M.J. Savage, Phys. Rev. C 68, 065802 (2003) arXiv:nucl-th/0305032
L.B. Leinson, Phys. Rev. C 85, 065502 (2012) arXiv:1206.3648
L.B. Leinson, Phys. Rev. C 83, 055803 (2011) arXiv:1007.2803
L. di Gallo, M. Oertel, M. Urban, Phys. Rev. C 84, 045801 (2011) arXiv:1107.4209
C. Manuel, S. Sarkar, L. Tolos, Phys. Rev. C 90, 055803 (2014) arXiv:1407.7431
M. Mannarelli, C. Manuel, L. Tolos, Ann. Phys. (N.Y.) 336, 12 (2013) arXiv:1212.5152
C. Manuel, L. Tolos, Phys. Rev. D 84, 123007 (2011) arXiv:1110.0669
D.N. Aguilera, V. Cirigliano, J.A. Pons, S. Reddy, R. Sharma, Phys. Rev. Lett. 102, 091101 (2009) arXiv:0807.4754
K.P. Levenfish, D.G. Yakovlev, Astron. Lett. 20, 43 (1994)
A. Sedrakian, Phys. Lett. B 607, 27 (2005) arXiv:nucl-th/0411061
M.G. Alford, S. Reddy, K. Schwenzer, Phys. Rev. Lett. 108, 111102 (2012) arXiv:1110.6213
M.G. Alford, K. Pangeni, Phys. Rev. C 95, 015802 (2017) arXiv:1610.08617
M.G. Alford, S. Mahmoodifar, K. Schwenzer, Phys. Rev. D 85, 044051 (2012) arXiv:1103.3521
C. Petrovich, A. Reisenegger, Astron. Astrophys. 528, A66 (2011) arXiv:1008.3013
F. Wilczek, Phys. Rev. Lett. 40, 279 (1978)
S. Weinberg, Phys. Rev. Lett. 40, 223 (1978)
R.D. Peccei, H.R. Quinn, Phys. Rev. Lett. 38, 1440 (1977)
G. ’t Hooft, Phys. Rev. Lett. 37, 8 (1976)
G.G. Raffelt, Stars as Laboratories for Fundamental Physics (University of Chicago Press, Chicago, 1996)
G.G. Raffelt, Astrophysical axion bounds, in Axions, edited by M. Kuster, G. Raffelt, B. Beltrán, Lect. Notes Phys., Vol. 741 (Berlin Springer Verlag, 2008) p. 51 arXiv:hep-ph/0611350
M. Giannotti, I.G. Irastorza, J. Redondo, A. Ringwald, K. Saikawa, J. Cosmol. Astropart. Phys. 10, 010 (2017) arXiv:1708.02111
Particle Data Group Collaboration (K.A. Olive et al.), Chin. Phys. C 38, 090001 (2014)
J.E. Kim, Phys. Rev. Lett. 43, 103 (1979)
M. Shifman, A. Vainshtein, V. Zakharov, Nucl. Phys. B 166, 493 (1980)
J. Keller, A. Sedrakian, Nucl. Phys. A 897, 62 (2013) arXiv:1205.6940
A. Sedrakian, Phys. Rev. D 93, 065044 (2016) arXiv:1512.07828
G. Volovik, The Universe in a Helium Droplet, International Series of Monographs on Physics, (OUP, Oxford, 2009)
P.-G. de Gennes, Superconductivity of Metals and Alloys (Advanced Book Program, Perseus Books, New York, N.Y., 1999)
C. Caroli, P.G. De Gennes, J. Matricon, Phys. Lett. 9, 307 (1964)
P.J. Feibelman, Phys. Rev. D 4, 1589 (1971)
F.V. de Blasio, O. Elgarøy, Phys. Rev. Lett. 82, 1815 (1999) arXiv:nucl-th/9808057
O. Elgarøy, F.V. De Blasio, Astron. Astrophys. 370, 939 (2001) arXiv:astro-ph/0102343
M. Machida, T. Koyama, Phys. Rev. Lett. 94, 140401 (2005)
C.-C. Chien, Y. He, Q. Chen, K. Levin, Phys. Rev. A 73, 041603 (2006) arXiv:cond-mat/0510647
M. Machida, T. Koyama, Y. Ohashi, Physica C 437, 190 (2006)
C. Caroli, J. Matricon, Phys. Kondens. Mater. 3, 380 (1965)
P.W. Anderson, N. Itoh, Nature 256, 25 (1975)
D. Pines, J. Shaham, M.A. Alpar, P.W. Anderson, Prog. Theor. Phys. Suppl. 69, 376 (1980)
R.I. Epstein, G. Baym, Astrophys. J. 328, 680 (1988)
P. Donati, P.M. Pizzochero, Nucl. Phys. A 742, 363 (2004)
P. Donati, P.M. Pizzochero, Phys. Lett. B 640, 74 (2006)
P. Avogadro, F. Barranco, R.A. Broglia, E. Vigezzi, Nucl. Phys. A 811, 378 (2008) arXiv:0804.1765
A.D. Sedrakian, Mon. Not. R. Astron. Soc. 277, 225 (1995)
B. Link, Phys. Rev. Lett. 102, 131101 (2009) arXiv:0807.1945
A. Bulgac, M.M. Forbes, R. Sharma, Phys. Rev. Lett. 110, 241102 (2013) arXiv:1302.2172
G. Wlazłowski, K. Sekizawa, P. Magierski, A. Bulgac, M.M. Forbes, Phys. Rev. Lett. 117, 232701 (2016) arXiv:1606.04847
E.B. Sonin, Dynamics of Quantised Vortices in Superfluids (Cambridge University Press, Cambridge, UK, 2016)
L. Bildsten, R.I. Epstein, Astrophys. J. 342, 951 (1989)
J.A. Sauls, D.L. Stein, J.W. Serene, Phys. Rev. D 25, 967 (1982)
A. Sedrakian, Phys. Rev. D 58, 021301 (1998) arXiv:astro-ph/9806156
M.G. Alford, F. Wilczek, Phys. Rev. Lett. 62, 1071 (1989)
M.G. Alford, A. Sedrakian, J. Phys. G 37, 075202 (2010) arXiv:1001.3346
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Sedrakian, A., Clark, J.W. Superfluidity in nuclear systems and neutron stars. Eur. Phys. J. A 55, 167 (2019). https://doi.org/10.1140/epja/i2019-12863-6
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DOI: https://doi.org/10.1140/epja/i2019-12863-6