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arXiv:cond-mat/9409072 · Physical review. B, Condensed matter

Master equation for a particle coupled to a two-level reservoir

Paulo C. Marques, A. H. Castro Neto

Published Oct 15, 1995• 1 citation
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Abstract

We study the quantum dissipative dynamics of a particle coupled linearly to a set of two-level systems (the heat bath) via the master equation method, which we extract from the path integral formalism independently from the form of the bath spectral density. We compare our results with the standard models based on bosonic heat baths, showing their main differences and similarities. In particular, we study special forms for the spectral density of the bath which give results quite different from the standard models.

DOI
10.1103/physrevb.52.10693

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The dynamical behavior of a two-level system coupled linearly to a dissipative bath of two-level systems whose tunneling splittings and coupling parameters are distributed according to an Ohmic spectrum is studied using numerical path integral methods as well as the noninteracting blip approximation for an equivalent harmonic environment characterized by a scaled spectral density. Comparisons with the behaviors of the conventional spin-boson model of similar coupling strength reveal a weaker quenching of coherence in the present case. Finally, the boundary in parameter space between coherent and incoherent dynamics is mapped.
We consider the reduced dynamics in a bipartite quantum system (consisting of a central system and an intermediate environment) coupled to a heat bath at finite temperature. To describe this situation, in the simplest possible---yet physically meaningful---way, we introduce the ``depolarizing heat bath'' as a minimal dissipation model. We conjecture that, at sufficiently strong dissipation, any other dissipation model implemented in the form of a Markovian quantum master equation will yield the same reduced dynamics of the central system as the minimal model. To support this conjecture, we study a two-level system coupled to an oscillator mode. For the coupling between the two parts, we consider the Jaynes-Cummings or a dephasing coupling, while the coupling to the heat bath is modeled by the quantum optical or the Caldeira-Leggett master equation (neglecting any direct coupling between central system and heat bath). We then provide ample numerical evidence for both model independence and accuracy of the depolarizing heat bath model. Alongside our study, we investigate different regimes, where the strong-coupling condition leads to coherence and/or population stabilization.
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We investigate a system of two interacting qubits having one of them isolated and the other coupled to a thermal reservoir. We consider two different models of system-reservoir interaction: i) a model, in which the master equation is derived taking into account the interaction between the two subsystems (qubits), ii) a naive model, in which the master equation consists of a dissipative term added to the unitary evolution term. We study the dynamics of quantities such as bipartite entanglement, quantum discord and the linear entropy of the isolated qubit for both strong and weak coupling regimes (qubit-qubit interaction) as well as for different temperatures of the reservoir. We find significant disagreements between the results obtained from the two models even in the weak coupling regime. For instance, we show that according to the phenomenological model, the isolated qubit would approach a maximally mixed state more slowly for higher temperatures (unphysical result), while the microscopic model predicts the opposite behaviour (correct result).