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Theoretical and Mathematical Physics

Application of the method of nonequilibrium thermodynamic potentials to systems of fermions interacting with bosons

A. P. Grigin, É.L. Nagaev

Published Mar 1, 1974• 2 citations
Publisher
DOI
10.1007/bf01035650

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We develop a superoperator coupled cluster method for nonequilibrium open many-body quantum systems described by the Lindblad master equation. The method is universal and applicable to systems of interacting fermions, bosons or their mixtures. We present a general theory and consider its application to the problem of quantum transport through the system with electron–phonon correlations. The results are assessed against the perturbation theory and nonequilibrium configuration interaction theory calculations.
This chapter derives from first principles the time-dependent Gross–Pitaevskii equation, which describes the time-dependent behavior of the condensate wave function associated with the composite bosons that form on the BEC side of the BCS–BEC crossover at sufficiently low temperature. The derivation relies on the Green’s functions method for nonequilibrium problems developed before and explores the assumption that the fermionic chemical potential, associated with the initial preparation of the system at thermodynamic equilibrium, is the largest energy scale in the problem. The relation between the scattering length for composite bosons and the scattering length for the constituent fermions is also discussed.