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Physical review. E

Non-Markovian dynamics of fermionic and bosonic systems coupled to several heat baths

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

Published Mar 28, 2018• 7 citations
Publisher

Abstract

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.

DOI
10.1103/physreve.97.032134

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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.
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.
The non-Markovian Langevin approach is applied to study the dynamics of fermionic (bosonic) oscillator linearly coupled to a fermionic (bosonic) environment. The analytical expressions for occupation numbers in two different types of couplings (rotating-wave approximation and fully coupled) are compared and discussed. The weak-coupling and high- and low-temperature limits are considered as well. The conditions under which the environment imposes its thermal equilibrium on the collective subsystem are discussed. The sameness of the results, obtained with both the Langevin approach and the discretized environment method are shown. Short- and long-time nonequilibrium dynamics of fermionic and bosonic open quantum systems are analyzed both analytically and numerically.
The system of nonlinear Langevin equations was obtained by using Hamiltonian's operator of two coupling quantum oscillators which are interacting with heat bath. By using the analytical solution of these equations, the analytical expressions for transport coefficients was found. Generalized Langevin equations and fluctuation-dissipation relations are derived for the case of a nonlinear non-Markovian noise. The explicit expressions for the time-dependent friction and diffusion coefficients are presented for the case of linear couplings in the coordinate between the collective two coupled harmonic oscillators and heat 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.
The dynamics of a two-state system coupled to the dissipative degrees of freedom of the environment appears in many different contexts. In this paper we have given a general formulation of the problem as well as a detailed comparison of two a priori very different heat baths: (a) a collection of harmonic oscillators coupled to the system, and (b) a collection of fermions coupled to the system. Consideration of such heat baths is motivated by the assertion that the weakly excited states of the environment can be modeled by a collection of elementary excitations following Landau. Our conclusion is that the case of Ohmic dissipation of harmonic-oscillator heat bath is very similar to the fermionic bath, although a crucially important dimensionless parameter \ensuremath{\alpha} assumes a different range of values in the two different cases.