Dzhioev, Alan A., and Kosov, D.S. (2012) Nonequilibrium perturbation theory in Liouville–Fock space for inelastic electron transport. Journal of Physics: Condensed Matter, 24. 22534. p. 225304.

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Abstract

We use a superoperator representation of the quantum kinetic equation to develop nonequilibrium perturbation theory for an inelastic electron current through a quantum dot. We derive a Lindblad-type kinetic equation for an embedded quantum dot (i.e. a quantum dot connected to Lindblad dissipators through a buffer zone). The kinetic equation is converted to non-Hermitian field theory in Liouville–Fock space. The general nonequilibrium many-body perturbation theory is developed and applied to the quantum dot with electron–vibronic and electron–electron interactions. Our perturbation theory becomes equivalent to a Keldysh nonequilibrium Green's function perturbative treatment provided that the buffer zone is large enough to alleviate the problems associated with approximations of the Lindblad kinetic equation.

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