 | This article needs attention from an expert in physics. The specific problem is: Keldysh formalism is around for quite a while. One should cite some original work or review articles/books. Furthermore, Keldysh formalism is far more versatile than indicated in the article in its present form. (June 2011) |
 | This article includes a list of general references, but it lacks sufficient corresponding inline citations. (June 2011) |
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In non-equilibrium physics, the Keldysh formalism or Keldysh–Schwinger formalism is a general framework for describing the quantum mechanical evolution of a system in a non-equilibrium state or systems subject to time varying external fields (electrical field, magnetic field etc.). Historically, it was foreshadowed by the work of Julian Schwinger and proposed almost simultaneously by Leonid Keldysh[1] and, separately, Leo Kadanoff and Gordon Baym.[2] It was further developed by later contributors such as O. V. Konstantinov and V. I. Perel.[3]
Extensions to driven-dissipative open quantum systems is given not only for bosonic systems,[4] but also for fermionic systems.[5]
The Keldysh formalism provides a systematic way to study non-equilibrium systems, usually based on the two-point functions corresponding to excitations in the system. The main mathematical object in the Keldysh formalism is the non-equilibrium Green's function (NEGF), which is a two-point function of particle fields. In this way, it resembles the Matsubara formalism, which is based on equilibrium Green functions in imaginary-time and treats only equilibrium systems.
- ^ Keldysh, Leonid (1965). "Diagram technique for nonequilibrium processes". Sov. Phys. JETP. 20: 1018.
- ^ Kadanoff, Leo; Baym, Gordon (1962). Quantum statistical mechanics. New York. ISBN 020141046X.
{{cite book}}: CS1 maint: location missing publisher (link) - ^ Kamenev, Alex (2011). Field theory of non-equilibrium systems. Cambridge: Cambridge University Press. ISBN 9780521760829. OCLC 721888724.
- ^ Sieberer, Lukas; Buchhold, M; Diehl, S (2 August 2016). "Keldysh field theory for driven open quantum systems". Reports on Progress in Physics. 79 (9): 096001. arXiv:1512.00637. Bibcode:2016RPPh...79i6001S. doi:10.1088/0034-4885/79/9/096001. PMID 27482736. S2CID 4443570.
- ^ Müller, Thomas; Gievers, Marcel; Fröml, Heinrich; Diehl, Sebastian; Chiocchetta, Alessio (2021). "Shape effects of localized losses in quantum wires: Dissipative resonances and nonequilibrium universality". Physical Review B. 104 (15): 155431. arXiv:2105.01059. Bibcode:2021PhRvB.104o5431M. doi:10.1103/PhysRevB.104.155431. S2CID 233481829.