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arXiv:2012.08123 · Physical review. E

Applicability of the absence of equilibrium in quantum system fully coupled to several fermionic and bosonic heat baths

Vazgen Valerikovich Sargsyan, A. A. Hovhannisyan, G. G. Adamian, N. V. Antonenko, Denis Lacroix A

Published Jan 29, 2021• 3 citations
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Abstract

The time evolution of an occupation number is studied for a fermionic or bosonic oscillator linearly fully coupled to several fermionic and bosonic heat baths. The influence of the characteristics of thermal reservoirs of different statistics on the nonstationary population probability is analyzed at large times. Applications of the absence of equilibrium in such systems for creating a dynamic (nonstationary) memory storage are discussed.

DOI
10.1103/physreve.103.012137

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The time evolution of an occupation number is studied for a fermionic or bosonic oscillator linearly fully coupled to several fermionic and bosonic heat baths. The influence of the characteristics of thermal reservoirs of different statistics on the nonstationary population probability is analyzed at large times. Applications of the absence of equilibrium in such systems for creating a dynamic (nonstationary) memory storage are discussed.
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Employing the fermionic and bosonic Hamiltonians for the collective oscillator linearly FC-coupled with several heat baths, the analytical expressions for the collective occupation number are derived within the non-Markovian quantum Langevin approach. The master equations for the occupation number of collective subsystem are derived and discussed. In the case of Ohmic dissipation with Lorenzian cutoffs, the possibility of reduction of the system with several heat baths to the system with one heat bath is analytically demonstrated. For the fermionic and bosonic systems, a comparative analysis is performed between the collective subsystem coupled to two heat baths and the reference case of the subsystem coupled to one bath.
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.
We developed this work at the moment with the objective to resolver the master equation for both thermal reservoir: bosonic and fermionic, as well as the master equation in reservoirs of vacuum and of Fock compressed . the bosonic thermal reservoir is modeled by a collection of coupled harmonic oscillators and the fermionic reservoir by a collection of two-level atoms. We made use of the Jaynes-Cummings model and the Bohr, Bohr-Markov and Markov approaches. In the end we discussed the application to the master equation for two distinct phenomena, Cooling by Heating (CBH) analyzing average energy graphs to the atomic system versus number of photons, and the average energy of the bosonic system as a function of the mean number of phonons, we observed the negative temperature in the absolute scale due to the inversion of population of states in function of cooperativity, we also analyzed a signature of negative response in a three level system interacting in a optical cavity, that comes as a result of decrease in the output field intensity when the input field intensity is increased.
Employing quadratic fermionic and bosonic Hamiltonians for collective and internal subsystems with a linear rotating-wave-approximation coupling, we studied the role of heat-bath statistics on the dynamics of the collective motion. The master equations for the collective occupation number derived directly from the quadratic Hamiltonians and within the Non-Markovian Langevin approach are discussed and their solutions are obtained. Because of the different nature of the heat-bath statistics, the path to equilibrium or the relaxation time is affected as shown in the numerical calculations.