Description of non-Markovian effect in open quantum system with the discretized environment method

Abstract

An approach, called discretized environment method, is introduced to treat exactly non-Markovian effects in open quantum systems. In this approach, a complex environment described by a spectral function is mapped into a finite set of discretized states with an appropriate coupling to the system of interest. The finite set of system plus environment degrees of freedom are then explicitly followed in time leading to a quasi-exact description. The present approach is anticipated to be particularly accurate in the low temperature and strongly non-Markovian regime. The discretized environment method is validated on a two-level system (qubit) coupled to a bosonic or fermionic heat bath. A perfect agreement with the quantum Langevin approach is found. Further illustrations are made on a three-level system (qutrit) coupled to a bosonic heat-bath. Emerging processes due to strong memory effects are discussed.

Non-Markovian dynamics of fully coupled fermionic and bosonic oscillators

“…Many problems in various open quantum systems can be described by using the Langevin equations in the space of relevant collective coordinates. The results of the Langevin approach were confirmed by considering the dynamics of an open quantum system with the discretized environment method (DEM) [28] which allows us to incorporate environment explicitly in a discretized form.…”

“…As a cross-check of the analytical solutions given above, we also applied the discretized environment method [28] generalized to treat the FC case. The simple idea developed in this method is that the continuous environment can be accurately discretized so that the equations of motion are solved by a direct diagonalization of the complete (collective subsystem + environment) Hamiltonian.…”

“…The discretization procedure is described in Ref. [28] and we only give below novel aspects associated with the FC case compared with the RWA case. L is a 4 × 4 block matrix with…”

“…Models describing the interaction between fermionic systems and spin degrees of freedom play an important role [7,11,12,[17][18][19]26]. In particular, an approach of these systems to equilibrium would greatly help to understand how they can reach the thermodynamic limits and how the thermalizations of the isolated system and the collective subsystem of this isolated system are related [27,28]. It is interesting to study the crossover from coherent to incoherent dynamics in the damped quantum system [29].…”

“…[41] and consider the general case of a fully coupled (FC) oscillator modeling fermionic (bosonic) collective subsystem coupled with a fermionic (bosonic) heat bath. The results obtained will be checked with the DEM [28] extended to treat FC oscillator and compared with those obtained in the RWA case.…”