Abstract
The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to describe in an unified manner diverse physical phenomena including coexisting superconductivity and insulators in (quasi)one-dimensional systems, superconductivity and Coulomb blockade in granular superconductors and Josephson networks, Anderson localization and mesoscopic effects in disordered and chaotic systems, and thermodynamic quantum time-space crystals.
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REFERENCES
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 5: Statistical Physics (Pergamon, Oxford, 1980).
K. G. Wilson, Phys. Rev. B 4, 3174 (1971).
A. Z. Patashinskii and V. L. Pokrovskii, Sov. Phys. JETP 23, 292 (1964).
L. P. Kadanoff, Physics (Amsterdam, Neth.) 2, 263 (1966).
A. I. Larkin and D. E. Khmelnitskii, Sov. Phys. JETP 29, 1123 (1969).
K. B. Efetov and A. I. Larkin, Sov. Phys. JETP 42, 390 (1976).
F. D. M. Haldane, J. Phys. C 14, 2585 (1981).
A. O. Gogolin, A. A. Nersesyan, and A. M. Tsvelik, Bosonization and Strongly Correlated Systems (Cambridge Univ. Press, New York, 2004).
K. B. Efetov, Sov. Phys. JETP 51, 1015 (1980).
I. S. Beloborodov, A. V. Lopatin, V. M. Vinokur, and K. B. Efetov, Rev. Mod. Phys. 79, 469 (2007).
F. Wegner, Z. Phys. B 35, 207 (1979).
K. B. Efetov, A. I. Larkin, and D. E. Khmelnitskii, Sov. Phys. JETP 52, 568 (1980).
K. B. Efetov, Sov. Phys. JETP 55, 514 (1982).
K. B. Efetov, Adv. Phys. 32, 53 (1983).
K. B. Efetov, Supersymmetry in Disorder and Chaos (Cambridge Univ. Press, New York, 1997).
F. Wilczek, Phys. Rev. Lett. 109, 160401 (2012).
H. Watanabe and M. Oshikawa, Phys. Rev. Lett. 114, 251603 (2015).
K. B. Efetov, arXiv:1902.07520.
K. B. Efetov and A. I. Larkin, Sov. Phys. JETP 39, 1129 (1974).
I. E. Dzyaloshinskii, and A. I. Larkin, Sov. Phys. JETP 38, 202 (1974).
A. Luther and I. Peschel, Phys. Rev. B 9, 2911 (1974).
A. Luther and V. Emery, Phys. Rev. Lett. 33, 589 (1974).
K. B. Efetov and A. Tschersich, Phys. Rev. B 67, 174205 (2003).
P. W. Anderson, Phys. Rev. 109, 1492 (1958).
A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinskii, Methods of Quantum Field Theory in Statistical Physics (Prentice Hall, New York, 1963).
V. L. Berezinsky, Sov. Phys. JETP 38, 620 (1974).
L. P. Gorkov and G. M. Eliashberg, Sov. Phys. JETP 21, 1940 (1965).
E. Wigner, Ann. Math. 53, 36 (1951);
Ann. Math. 67, 325 (1958).
F. J. Dyson, J. Math. Phys. 3, 140 (1962);
J. Math. Phys. 3, 157 (1962);
J. Math. Phys. 3, 166 (1962);
J. Math. Phys. 3, 1199 (1962).
E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).
L. P. Gorkov, A. I. Larkin, and D. E. Khmelnitskii, Sov. Phys. JETP Lett. 30, 228 (1979).
E. Abrahams, P. W. Anderson, and T. V. Ramakrishnan, Philos. Mag. 42, 827 (1980).
E. Abrahams and T. V. Ramakrishnan, J. Non-Cryst. Solids 35, 15 (1980).
L. Schäfer and F. Wegner, Z. Phys. B 38, 113 (1980).
A. M. Finkelstein, Sov. Phys. JETP 57, 97 (1983).
A. M. M. Pruisken, Nucl. Phys. B 235, 277 (1984).
K. B. Efetov, Sov. Phys. JETP 55, 514 (1982).
K. B. Efetov, Sov. Phys. JETP 56, 467 (1982);
J. Phys. C 15, L909 (1982).
J. J. M. Verbaarschot, H. A. Weidenmüller, and M. R. Zirnbauer, Phys. Rep. 129, 367 (1985).
O. Bohigas, M. J. Gianonni, and C. Schmidt, Phys. Rev. Lett. 52, 1 (1984);
J. Phys. Lett. 45, L1015 (1984).
Supersymmetry and Trace Formula, Ed. by J. P. Keating, D. E. Khmelnitskii, and I. V. Lerner, Vol. 370 of NATO ASI, Ser. B: Physics (Kluwer Academic, New York, 1999).
C. W. J. Beenakker, Rev. Mod. Phys. 69, 733 (1997).
B. L. Altshuler and B. I. Shklovskii, Sov. Phys. JETP 64, 127 (1986).
K. B. Efetov and A. I. Larkin, Sov. Phys. JETP 58, 444 (1983).
K. B. Efetov, Sov. Phys. JETP Lett. 40, 738 (1984);
Sov. Phys. JETP 61, 606 (1985).
M. R. Zirnbauer, Nucl. Phys. B 265 (FS15), 375 (1986);
Phys. Rev. B 34, 6394 (1986).
K. B. Efetov, Sov. Phys. JETP 65, 360 (1987).
K. B. Efetov, Sov. Phys. JETP 66, 634 (1987).
K. B. Efetov, Sov. Phys. JETP 67, 199 (1988).
T. Guhr, A. Müller-Groeling, and H. A. Weidenmüller, Phys. Rep. 299, 190 (1998).
A. D. Mirlin, Phys. Rep. 326, 259 (2000).
F. Evers and A. D. Mirlin, Rev. Mod. Phys. 80, 1355 (2008).
50 years of Anderson Localization, Ed. by E. Abrahams (World Scientific, Singapore, 2010).
P. Bruno, Phys. Rev. Lett. 110, 118901 (2013).
F. Wilczek, Phys. Rev. Lett. 110, 118902 (2013).
T. Li, Z.-X. Gong, Z.-Q. Yin, H. T. Quan, X. Yin, P. Zhang, L.-M. Duan, and X. Zhang, Phys. Rev. Lett. 109, 163001 (2012).
P. Bruno, Phys. Rev. Lett. 111, 029301 (2013).
P. Bruno, Phys. Rev. Lett. 111, 070402 (2013).
P. Nozieres, Europhys. Lett. 103, 57008 (2013).
F. Wilczek, Phys. Rev. Lett. 111, 250402 (2013).
K. Sacha, Phys. Rev. A 91, 033617 (2015).
V. Khemani, A. Lazarides, R. Moessner, and S. L. Sondhi, Phys. Rev. Lett. 116, 250401 (2016).
C. W. von Keyserlingk, V. Khemani, and S. L. Sondhi, Phys. Rev. B 94, 085112 (2016).
D. V. Else, B. Bauer, and C. Nayak, Phys. Rev. Lett. 117, 090402 (2016).
N. Y. Yao, A. C. Potter, I.-D. Potirniche, and A. Vishwanath, Phys. Rev. Lett. 118, 030401 (2017).
S. Autti, V. B. Eltsov, and G. E. Volovik, Phys. Rev. Lett. 120, 215301 (2018).
J. Zhang, P. W. Hess, A. Kyprianidis, P. Becker, A. Lee, J. Smith, G. Pagano, I. D. Potirniche, A. C. Potter, A. Vishwanath, N. Y. Yao, and C. Monroe, Nature (London, U.K.) 543, 217 (2017).
S. Choi, J. Choi R. Landig, G. Kucsko, H. Zhou, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, V. Khemani, C. von Keyserlingk, N. Y. Yao, E. Demler, and M. D. Lukin, Nature (London, U.K.) 543, 221 (2017).
J. Bardeen, L. N. Cooper, and J. R. Schriefler, Phys. Rev. 108, 1175 (1957).
P. A. Volkov and K. B. Efetov, Phys. Rev. B 93, 085131 (2016).
P. A. Volkov and K. B. Efetov, J. Supercond. Nov. Magn. 29, 1069 (2016).
P. A. Volkov and K. B. Efetov, Phys. Rev. B 97, 165125 (2018).
S. Chakravarty, R. B. Laughlin, D. K. Morr, and C. Nayak, Phys. Rev. B 63, 094503 (2001).
S. I. Mukhin, J. Supercond. Nov. Mag. 22, 75 (2009).
S. I. Mukhin, J. Supercond, Nov. Mag. 24, 1165 (2011).
S. I. Mukhin, Condens. Matter 3, 39 (2018).
S. A. Brazovskii, S. A. Gordyunin, and N. N. Kirova, JETP Lett. 31, 487 (1980).
M. Abramowitz and A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).
A. F. Volkov and Sh. M. Kogan, Sov. Phys. JETP 38, 1018 (1974).
R. A. Barankov, L. S. Levitov, and B. Z. Spivak, Phys. Rev. Lett. 93, 160401 (2004).
R. A. Barankov and L. S. Levitov, Phys. Rev. Lett. 96, 230403 (2006).
E. A. Yuzbashyan, B. L. Altshuler, V. B. Kuznetsov, and V. Z. Enolskii, Phys. Rev. B 72, 220503(R) (2005).
E. A. Yuzbashyan, B. L. Altshuler, V. B. Kuzentsov, and V. Z. Enolskii, J. Phys. A: Math. Gen. 38, 7831 (2005).
E. A. Yuzbashyan and M. Dzero, Phys. Rev. Lett. 96, 230404 (2006).
A. Moor, A. F. Volkov, and K. B. Efetov, Phys. Rev. Lett. 118, 047001 (2017).
N. S. Headings, S. M. Hayden, J. Kulda, N. H. Babu, and D. A. Cardwell, Phys. Rev. B 84, 104513 (2011).
ACKNOWLEDGMENTS
Financial support of Deutsche Forschungsgemeinschaft (Projekt EF 11/10-1) and of the Ministry of Science and Higher Education of the Russian Federation in the framework of Increase Competitiveness Program of NUST “MISiS” (no. K2-2017-085”) is greatly appreciated.
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Contribution for the JETP special issue in honor of I. M. Khalatnikov’s 100th anniversary
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Efetov, K.B. Order Parameter in Electron System: Its Fluctuations and Oscillations. J. Exp. Theor. Phys. 129, 680–692 (2019). https://doi.org/10.1134/S1063776119100030
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DOI: https://doi.org/10.1134/S1063776119100030