A new method for quantum processes in fermionic heat baths

A. A. Hovhannisyan, Vazgen Valerikovich Sargsyan, G. G. Adamian +2 more

Denis Lacroix A, Vazgen Valerikovich Sargsyan, G. G. Adamian +2 more

A method is proposed to describe Fermi or Bose systems coupled to one or several heat baths composed of fermions and/or bosons. The method, called the coupled equations of motion method, properly includes non-Markovian effects. The approach is exact in the full-coupling approximation when only bosonic particles are present in the system and baths. The approach provides an approximate treatment when fermions are present either in the system and/or in one or several environments. Our approach has the advantage of properly respecting the Pauli exclusion principle for fermions during the evolution. We illustrate the approach for the single fermionic or bosonic oscillator coupled to one or two heat baths assuming different types of quantum statistics (fermion or boson) for them. The cases of a Fermi system coupled to fermion or boson heat baths or a mixture of both are analyzed in detail. With the future goal of treating Fermi systems formed of an increasing number of two-level systems (qubits), we discuss possible simplifications that could be made in the equations of motion and their limits of validity in terms of the system-bath coupling or of the initial heat bath temperatures.

Florian Marquardt

Jürgen Berges, Szabolcs Borsányi, Julien Serreau

Erik M. Aurell

This paper is about quantum heat defined as the change in energy of a bath during a process. The presentation takes into account recent developments in classical strong-coupling thermodynamics and addresses a version of quantum heat that satisfies quantum-classical correspondence. The characteristic function and the full counting statistics of quantum heat are shown to be formally similar. The paper further shows that the method can be extended to more than one bath, e.g., two baths at different temperatures, which opens up the prospect of studying correlations and heat flow. The paper extends earlier results on the expected quantum heat in the setting of one bath [E. Aurell and R. Eichhorn, New J. Phys. 17, 065007 (2015)NJOPFM1367-263010.1088/1367-2630/17/6/065007; E. Aurell, Entropy 19, 595 (2017)ENTRFG1099-430010.3390/e19110595].

P. Nielaba, Joel L. Lebowitz, Herbert E. Spohn +1 more