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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.
In non-equilibrium physics, the Keldyshformalism or Keldysh–Schwinger formalism is a general framework for describing the quantum mechanical evolution...
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collisions. Keldyshformalism (a.k.a. NEGF—non-equilibrium Green functions): A quantum approach to including stochastic dynamics is found in the Keldysh formalism...
See for example the book: Also, it has been demonstrated that the Keldyshformalism provides a viable alternative to the replica approach. The first of...
to one loop without an explicit regulator. Schwinger believed in the formalism of local fields, while Feynman had faith in the particle paths. They followed...
a real-time formalism which come in two forms. A path-ordered approach to real-time formalisms includes the Schwinger–Keldyshformalism and more modern...
the 1950s and 1960s Leonid Keldysh – a theoretical physicist known for developing the Keldyshformalism Mstislav Keldysh - a Soviet mathematician who...
I. Perel, Leo Kadanoff and Gordon Baym, and Leonid Keldysh independently develop Keldyshformalism. 1962: Jeffrey Goldstone, Yoichiro Nambu, Abdus Salam...
field approximation (SFA), or Keldysh-Faisal-Reiss theory is a physical model, started in 1964 by the Russian physicist Keldysh, is currently used to describe...
an elegant formalism based on the non-equilibrium Green's functions of Leo Kadanoff and Gordon Baym, and independently by Leonid Keldysh was advanced...
pp. 208–210. Hordiychuk 1989c, p. 174. Hordiychuk 1989c, pp. 157–166. Keldysh, Yuri Vsevolodovich, ed. (1990). "Lysenko, Nikolai Vitalievich". Encyclopedic...
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