Geodesic
Kinetic coefficients in a time-dependent Green's function formalism at finite temperature
Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 3, pp. 538-554 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We discuss microscopic foundations of dissipation arising in a model Fermi or Bose system with weak local interaction. We consider the dynamics of equilibrium fluctuations in the Keldysh–Schwinger formalism and discuss the relation between dissipation and pinch singularities of perturbation theory diagrams. Using the Dyson equation, we define and calculate the dissipation parameter in the two-loop approximation. We show that this parameter is analogous to Onsager's kinetic coefficient and is associated with decay in the quasiparticle spectrum.
Keywords: quantum field theory, statistical mechanics, time-dependent Green's functions at finite temperature, kinetic coefficient. 
@article{TMF_2022_213_3_a9,
     author = {V. A. Krivorol and M. Yu. Nalimov},
     title = {Kinetic coefficients in a~time-dependent {Green's} function formalism at finite temperature},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {538--554},
     year = {2022},
     volume = {213},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_213_3_a9/}
}
TY  - JOUR
AU  - V. A. Krivorol
AU  - M. Yu. Nalimov
TI  - Kinetic coefficients in a time-dependent Green's function formalism at finite temperature
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2022
SP  - 538
EP  - 554
VL  - 213
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2022_213_3_a9/
LA  - ru
ID  - TMF_2022_213_3_a9
ER  - 
%0 Journal Article
%A V. A. Krivorol
%A M. Yu. Nalimov
%T Kinetic coefficients in a time-dependent Green's function formalism at finite temperature
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2022
%P 538-554
%V 213
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2022_213_3_a9/
%G ru
%F TMF_2022_213_3_a9
V. A. Krivorol; M. Yu. Nalimov. Kinetic coefficients in a time-dependent Green's function formalism at finite temperature. Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 3, pp. 538-554. http://geodesic.mathdoc.fr/item/TMF_2022_213_3_a9/

[1] D. P. Zubarev, V. G. Morozov, G. Repke, Statisticheskaya mekhanika neravnovesnykh protsessov, v. 1, Fizmatlit, M., 2002 | Zbl

[2] D. P. Zubarev, V. G. Morozov, G. Repke, Statisticheskaya mekhanika neravnovesnykh protsessov, v. 1, Fizmatlit, M., 2002 | Zbl

[3] T. Brauner, S. Hartnoll, P. Kovtun, H. Liu, M. Mezei, A. Nicolis, R. Penco, S.-H. Shao, D. T. Son, Snowmass white paper: effective field theories for condensed matter systems, arXiv: 2203.10110

[4] M. Bluhm, A. Kalweit, M. Nahrgang et al., “Dynamics of critical fluctuations: Theory – phenomenology – heavy-ion collisions”, Nucl. Phys. A, 1003 (2020), 122016, 64 pp., arXiv: 2001.08831 | DOI

[5] R. P. Feynman, F. L. Vernon, Jr., “The theory of a general quantum system interacting with a linear dissipative system”, Ann. Phys., 24 (1963), 118–173 | DOI | MR

[6] M. Patriarca, “Feynman Vernon model of a moving thermal environment”, Phys. E, 29:1 (2005), 243–250 | DOI

[7] U. Weiss, Quantum Dissipative Systems, Series in Modern Condensed Matter Physics, 13, World Sci., Singapore, 2008 | MR

[8] Á. Rivas, S. F. Huelga, Open Quantum Systems. An Introduction, Springer Briefs in Physics, Springer, Berlin, Heidelberg, 2012 | DOI | MR

[9] G. Lindblad, “On the generators of quantum dynamical semigroups”, Commun. Math. Phys., 48:2 (1976), 119–130 | DOI | MR

[10] V. Gorini, A. Kossakowski, E. C. G. Sudarshan, “Completely positive dynamical semigroups of $N$-level systems”, J. Math. Phys., 17:5 (1976), 821–825 | DOI | MR

[11] F. Nathan, M. S. Rudner, “Universal Lindblad equation for open quantum systems”, Phys. Rev. B, 102:11 (2020), 115109, 24 pp., arXiv: ; Erratum, 104 (2021), 119901, 2 pp. 2004.01469 | DOI | DOI

[12] V. Tarasov, Quantum Mechanics of Non-Hamiltonian and Dissipative Systems, Monograph Series On Nonlinear Science and Complexity, 7, Elsevier, Amsterdam, 2008 | MR

[13] R. Kubo, “Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems”, J. Phys. Soc. Japan, 12:6 (1957), 570–586 | DOI | MR

[14] R. Kubo, M. Yokota, S. Nakajima, “Statistical-mechanical theory of irreversible processes. II. Response to thermal disturbance”, J. Phys. Soc. Japan, 12:11 (1957), 1203–1211 | DOI | MR

[15] M. Mouas, J.-G. Gasser, S. Hellal, B. Grosdidier, A. Makradi, S. Belouettar, “Diffusion and viscosity of liquid tin: Green–Kubo relationship-based calculations from molecular dynamics simulations”, J. Chem. Phys., 136:9 (2012), 094501, 16 pp. | DOI

[16] Pu Liu, E. Harder, B. J. Berne, “On the calculation of diffusion coefficients in confined fluids and interfaces with an application to the liquid–vapor interface of water”, J. Phys. Chem. B, 108:21 (2004), 6595–6602 | DOI

[17] N. A. Volkov, M. V. Posysoev, A. K. Shchekin, “The effect of simulation cell size on the diffusion coefficient of an ionic surfactant aggregate”, Colloid J., 80:3 (2018), 248–254 | DOI

[18] L. Ts. Adzhemyan, F. M. Kuni, T. Yu. Novozhilova, “Nelineinoe obobschenie metoda proektiruyuschikh operatorov Mori”, TMF, 18:3 (1974), 383–392 | DOI | MR | Zbl

[19] G. M. Eliashberg, “Kineticheskoe uravnenie dlya vyrozhdennoi sistemy fermi-chastits,”, ZhETF, 41:4, 1241–1251 | MR

[20] P. I. Arseev, “O diagrammnoi tekhnike dlya neravnovesnykh sistem: vyvod, nekotorye osobennosti i nekotorye primeneniya”, UFN, 185:12 (2015), 1271–1321 | DOI | DOI

[21] L. M. Sieberer, A. Chiocchetta, A. Gambassi, U. C. Täuber, S. Diehl, “Thermodynamic equilibrium as a symmetry of the Schwinger–Keldysh action”, Phys. Rev. B, 92:13 (2015), 134307, 22 pp., arXiv: 1505.00912 | DOI

[22] A. N. Vasilev, Kvantovopolevaya renormgruppa v teorii kriticheskogo povedeniya i stokhasticheskoi dinamike, PIYaF, SPb., 1998 | DOI | MR | Zbl

[23] J. Honkonen, M. V. Komarova, Yu. G. Molotkov, M. Yu. Nalimov, “Effective large-scale model of boson gas from microscopic theory”, Nucl. Phys. B, 939 (2019), 105–129 | DOI

[24] M. F. Maghrebi, A. V. Gorshkov, “Nonequilibrium many-body steady states via Keldysh formalism”, Phys. Rev. B, 93:1 (2016), 014307, 15 pp., arXiv: 1507.01939 | DOI

[25] R. van Leeuwen, N. Dahlen, G. Stefanucci, C.-O. Almbladh, U. von Barth, “Introduction to the Keldysh formalism”, Time-Dependent Density Functional Theory, Lecture Notes in Physics, 706, eds. M. A. Marques, C. A. Ullrich, F. Nogueira, A. Rubio, K. Burke, E. K. Gross, Springer, Berlin, 2006, 33–59 | DOI

[26] F. M. Haehl, R. Loganayagam, M. Rangamani, “Schwinger–Keldysh formalism I: BRST symmetries and superspace”, JHEP, 2017:6 (2017), 69, 91 pp. | DOI | MR | Zbl

[27] M. J. B. Pereira, Keldysh field theory, University of Säo Paulo, Säo Paulo, 2019

[28] M. Geracie, F. M. Haehl, R. Loganayagam, P. Narayan, D. M. Ramirez, M. Rangamani, “Schwinger–Keldysh superspace in quantum mechanics”, Phys. Rev. D, 97:10 (2018), 105023, 17 pp., arXiv: 1712.04459 | DOI | MR

[29] A. Kamenev, A. Levchenko, “Keldysh technique and non-linear $\sigma$-model: basic principles and applications”, Adv. Phys., 58:3 (2009), 197–319, arXiv: 0901.3586 | DOI

[30] J. Rammer, Quantum Field Theory of Non-Equilibrium States, Cambridge Univ. Press, Cambridge, 2007 | DOI | MR

[31] J. Rammer, H. Smith, “Quantum field-theoretical methods in transport theory of metals”, Rev. Modern Phys., 58:2 (1986), 323–359 | DOI

[32] L. Kadanov, G. Beim, Kvantovaya statisticheskaya mekhanika. Metody funktsii Grina v teorii ravnovesnykh i neravnovesnykh protsessov, Mir, M., 1964 | DOI | MR | Zbl

[33] T. Tanaka, Y. Nishida, Thermal conductivity of a weakly interacting Bose gas by quasi-one dimensionality, arXiv: 2203.04936

[34] S. Jeon, “Hydrodynamic transport coefficients in relativistic scalar field theory”, Phys. Rev. D, 52:6 (1995), 3591–3642 | DOI

[35] S. Jeon, L. G. Yaffe, “From quantum field theory to hydrodynamics: Transport coefficients and effective kinetic theory”, Phys. Rev. D, 53:10 (1996), 5799–5809 | DOI

[36] Y. Hidaka, T. Kunihiro, “Renormalized linear kinetic theory as derived from quantum field theory: A novel diagrammatic method for computing transport coefficients”, Phys. Rev. D, 83:7 (2011), 076004, 18 pp., arXiv: 1009.5154 | DOI

[37] J. F. Nieves, S. Sahu, Taming the pinch singularities in the two-loop neutrino self-energy in a medium, arXiv: 2104.04459

[38] E. T. Akhmedov, U. Moschella, F. K. Popov, “Characters of different secular effects in various patches of de Sitter space”, Phys. Rev. D, 99:8 (2019), 086009, 15 pp. | DOI | MR

[39] E. T. Akhmedov, Ph. Burda, “Solution of the Dyson–Schwinger equation on a de Sitter background in the infrared limit”, Phys. Rev. D, 86:4 (2012), 044031, 10 pp., arXiv: 1202.1202 | DOI

[40] E. T. Akhmedov, F. K. Popov, V. M. Slepukhin, “Infrared dynamics of the massive $\phi_4$ theory on de Sitter space”, Phys. Rev. D, 88:2 (2013), 024021, 10 pp., arXiv: 1303.1068 | DOI

[41] E. T. Akhmedov, N. Astrakhantsev, F. K. Popov, “Secularly growing loop corrections in strong electric fields”, JHEP, 09 (2014), 71, 18 pp. | DOI

[42] A. A. Abrikosov, L. P. Gorkov, I. E. Dzyaloshinskii, Metody kvantovoi teorii polya v statisticheskoi fizike, Dobrosvet, M., 1998 | MR

[43] J. O. Andersen, “Theory of the weakly interacting Bose gas”, Rev. Modern Phys., 76:2 (2004), 599–639, arXiv: cond-mat/0305138 | DOI | MR

[44] Yu. Khonkonen, “Konturno uporyadochennye funktsii Grina v stokhasticheskoi teorii polya”, TMF, 175:3 (2013), 455–464 | DOI | DOI | MR | Zbl

[45] Yu. Khonkonen, M. V. Komarova, Yu. G. Molotkov, M. Yu. Nalimov, “Kineticheskaya teoriya bozonnogo gaza”, TMF, 200:3 (2019), 507–521 | DOI | DOI | MR

[46] A. N. Vasilev, Funktsionalnye metody v kvantovoi teorii polya i statistike, Izd-vo Leningr. un-ta, L., 1976

[47] Yu. A. Zhavoronkov, M. V. Komarova, Yu. G. Molotkov, M. Yu. Nalimov, Yu. Khonkonen, “Kriticheskaya dinamika fazovogo perekhoda v sverkhtekuchee sostoyanie”, TMF, 200:2 (2019), 361–377 | DOI | DOI | MR

[48] L. V. Keldysh, “Diagrammnaya tekhnika dlya neravnovesnykh protsessov”, ZhETF, 47:4 (1964), 1515–1527 | MR

[49] J. Schwinger, “Brownian motion of a quantum oscillator”, J. Math. Phys., 2:3 (1961), 407–432 | DOI | MR

[50] M. J. Hyrkäs, D. Karlsson, R. van Leeuwen, “Cutting rules and positivity in finite temperature many-body theory”, J. Phys. A: Math. Theor., 55:33 (2022), 335301, arXiv: 2203.11083 | DOI | MR

[51] R. C. Hwa, V. L. Teplitz, Homology and Feynman Integrals, Benjamin, New York, 1966 | MR

[52] H. W. Wyld, Jr., “Formulation of the theory of turbulence in an incompressible fluid”, Ann. Phys., 14 (1961), 143–165 | DOI | MR

[53] L. D. Landau, E. M. Lifshitz, Course of Theoretical Physics, v. 6, Fluid Mechanics, Elsevier, Amsterdam, 2013 | MR

[54] L. Ts. Adzhemyan, D. A. Evdokimov, M. Hnatič, E. V. Ivanova, M. V. Kompaniets, A. Kudlis, D. V. Zakharov, “Model A of critical dynamics: 5-loop expansion study”, Phys. A, 600 (2022), 127530, 17 pp. | DOI

[55] L. Ts. Adzhemyan, D. A. Evdokimov, M. Hnatič, E. V. Ivanova, M. V. Kompaniets, A. Kudlis, D. V. Zakharov, “The dynamic critical exponent z for 2d and 3d Ising models from five-loop $\varepsilon$ expansion”, Phys. Lett. A, 425 (2022), 127870, 6 pp., arXiv: 2111.04719 | DOI

[56] U. C. Täuber, Critical Dynamics: A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior, Cambridge Univ. Press, Cambridge, 2014 | DOI

[57] U. C. Täuber, “Renormalization group: applications in statistical physics”, Nucl. Phys. B: Proc. Suppl., 228 (2012), 7–34, arXiv: 1112.1375 | DOI | MR

[58] M. Gnatich, M. V. Komarova, M. Yu. Nalimov, “Mikroskopicheskoe obosnovanie stokhasticheskoi F-modeli kriticheskoi dinamiki”, TMF, 175:3 (2013), 398–407 | DOI | DOI | MR | Zbl

[59] A. M. Ilin, A. A. Ershov, “Asimptotika dvumernykh integralov, singulyarno zavisyaschikh ot malogo parametra”, Tr. IMM UrO RAN, 15:3 (2009), 116–126 | DOI | MR

[60] A. A. Ershov, M. I. Rusanova, “Asimptotika mnogomernykh integralov, singulyarno zavisyaschikh ot malogo parametra”, Tr. IMM UrO RAN, 22:1 (2016), 84–92 | DOI | MR

[61] A. M. Ilin, A. R. Danilin, Asimptoticheskie metody v analize, Fizmatlit, M., 2009 | Zbl

[62] R. D. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem, Dover Publ., New York, 2012 | MR

[63] J. Sulpizio, L. Ella, A. Rozen et al., “Visualizing Poiseuille flow of hydrodynamic electrons”, Nature, 576:7785 (2019), 75–79, arXiv: 1905.11662 | DOI

[64] K. Novoselov, A. K. Geim, S. Morozov et al., “Two-dimensional gas of massless Dirac fermions in graphene”, Nature, 438:7065 (2005), 197–200, arXiv: cond-mat/0509330 | DOI