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arXiv · 1804.10280

Chaos, Ergodicity and Equilibria in a Quantum Kac Model

Eric A. Carlen·Maria C. Carvalho·Michael P. Loss
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Abstract

We introduce quantum versions of the Kac Master Equation and the Kac Boltzmann Equation. We study the steady states of each of these equations, and prove a propagation of chaos theorem that relates them. The Quantum Kac Master Equation (QKME) describes a quantum Markov semigroup, while the Kac Boltzmann Equation describes a non-linear evolution of density matrices on the single particle state space. All of the steady states of the $N$ particle quantum system described by the QKME are separable, and thus the evolution described by the QKME is entanglement breaking. The results set the stage for a quantitative study of approach to equilibrium in quantum kinetic theory, and a quantitative study the rate of destruction of entanglement in a class of quantum Markov semigroups describing binary interactions.

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Eric A. Carlen, Maria C. Carvalho, Michael P. Loss. 2018-04-26. Chaos, Ergodicity and Equilibria in a Quantum Kac Model. https://arxiv.org/abs/1804.10280

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