Abstract
We consider a harmonic oscillator coupled to a Markovian environment, i.e. a thermal reservoir. We derive the Keldysh path integral and the corresponding lesser, greater, time-ordered, antitime-ordered, retarded, advanced, and Keldysh Green’s functions for this system. In order to give a conceptually clear derivation, we use the superoperator formalism and also define supercoherent states. The supercoherent states and the creation and annihilation superoperators provide a natural way to rewrite the master equation into a path integral.
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References
A. Perelomov, Generalized Coherent states and Their Applications, Springer (1986).
R. J. Glauber, Phys. Rev., 130, 2529 (1963).
L. Keldysh, Zh. Éksp. Teor. Fiz., 47, 1515 (1964).
A. Kamenev, Field Theory of Non-Equilibrium Systems, Cambridge University Press (2011).
J. S. Schwinger, J. Math. Phys., 2, 407 (1961).
R. Feynman and J. Vernon, Ann. Phys., 24, 118 (1963).
L. M. Sieberer, M. Buchhold, and S. Diehl, Rep. Prog. Phys., 79, 9 (2016).
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Kónya, G. Derivation of the Keldysh Path Integral from the Master Equation of a Harmonic Oscillator in a Thermal Bath Via Supercoherent States. J Russ Laser Res 39, 473–483 (2018). https://doi.org/10.1007/s10946-018-9742-0
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DOI: https://doi.org/10.1007/s10946-018-9742-0