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

TL;DR

This paper introduces a Coupled Equations of Motion method to model Fermi-Bose systems interacting with thermal baths, capturing non-Markovian effects and respecting fermionic principles, with applications to two-level systems and potential for larger quantum systems.

Contribution

The paper presents a novel, exact in full-coupling approximation method for bosonic systems and an approximate method for fermionic systems, incorporating non-Markovian dynamics and Pauli exclusion.

Findings

Method accurately models bosonic systems in full-coupling regime.

Approach respects Pauli exclusion principle for fermions.

Application to two-level systems with various bath compositions.

Abstract

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 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. The new approach has the advantage to properly respect the Pauli exclusion principle for fermions during the evolution. We illustrate the approach for the single Fermi or Bose two-level system coupled to one or two heat-baths assuming different types of quantum statistics (Fermion or Bosons) for them. The cases of Fermi system coupled to fermion or boson heat baths or a mixture of both are analyzed in details. With the future goal to treat Fermi systems formed of 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--baths coupling or of the initial heat baths temperatures.