Abstract
Understanding the behavior of a quantum system coupled to its environment is of fundamental interest in the general field of quantum technologies. It also has important repercussions on foundational problems in physics, such as the process of decoherence and the so-called quantum measurement problem. There have been many approaches to explore Markovian and non-Markovian dynamics within the framework of open quantum systems, but the richness of the ensuing dynamics is still not fully understood. In this paper we develop a non-Markovian extension of the standard Caldeira-Leggett model, based on expanding the dynamics of the reduced system at high temperature in inverse powers of the high-frequency cutoff of the Ohmic spectral density of the environment and derive a non-Markovian master equation for the reduced density matrix for the case of a general potential. We also obtain a fully analytical solution in the free particle case. While the short-time behavior of this solution does not diverge substantially from the Markovian behavior, at intermediate times we find a resurgence of coherence, which we name lateral coherence. We identify this with a corresponding transient negative entropy production rate, which is understood to be characteristic of non-Markovian dynamics. We also analyze the positivity of the reduced density matrix and derive the corresponding Fokker-Planck equation in the classical limit.
Highlights
The study of quantum systems in interaction with their environment—so-called open quantum systems—touches upon a number of unsolved problems in fundamental physics
In this paper we develop a non-Markovian extension of the standard Caldeira-Leggett model, based on expanding the dynamics of the reduced system at high temperature in inverse powers of the high-frequency cutoff of the Ohmic spectral density of the environment and derive a non-Markovian master equation for the reduced density matrix for the case of a general potential
We identify this with a corresponding transient negative entropy production rate, which is understood to be characteristic of non-Markovian dynamics
Summary
The study of quantum systems in interaction with their environment—so-called open quantum systems—touches upon a number of unsolved problems in fundamental physics. Both the adoption of general projection techniques [8,9,10] and the explicit calculation of specific environmental models [11] lead to reduced dynamics for the system of interest characterized by memory kernels, which account in principle for non-Markovian behavior. If ad hoc assumptions about the relaxation timescales of such memory kernels are made, a Markov approximation can be performed This leads to reduced quantum dynamics which are again Markovian and characterized by very fast (approximately exponential) decoherence of the coherent components [2], accounting thereby for the environment-induced measurement process [12,13], and the quantum-classical transition [14].
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