Non-Markovian dynamics of fully coupled fermionic and bosonic oscillators

Abstract

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. Shortand long-time nonequilibrium dynamics of fermionic and bosonic open quantum systems are analyzed both analytically and numerically.

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

“…The relaxation time of the heat-bath should be much less than the characteristic collective time. The similarity of expressions for the occupation numbers for fermionic and bosonic systems results from the similarity of the equations of motion for creation and annihilation operators [19,20].…”

“…Because the friction coefficient λ b (t) does not converge to a stationary value at t → +∞ (Fig. 1) [8,19], an asymptotic stationary value of occupation number n a in Eq. ( 13) can be reached if the condition…”

“…2) because the friction λ b (t) and, correspondingly, diffusion coefficient oscillate as a function of time (Fig. 1) [8,19]. To obtain Eq.…”

Non-Markovian modeling of Fermi-Bose systems coupled to one or several Fermi-Bose thermal baths

“…We follow here our previous work [21][22][23][24][25][26][27] and consider a Fermi or Bose system coupled to one or several baths. Some of the baths could be composed of fermions and some other of bosons.…”

“…In the following, we first recall some recent progress we have made in the description of systems coupled to several heat baths [21][22][23][24][25][26][27]. We then discuss in details the extra subtleties that appear for Fermi systems or environments compared to the Bose case.…”