Non-Markovian Dynamics Impact on the Foundations of Statistical Mechanics

Abstract

The foundations of statistical mechanics, namely how equilibrium hypothesis emerges microscopically from quantum theory, is explored through investigating the environment-induced quantum decoherence processes. Based on the recent results on non-Markovian dynamics [Phys. Rev. Lett. 109, 170402 (2012)], we find that decoherence of quantum states manifests unexpected complexities. Indeed, an arbitrary given initial quantum state, under the influence of different reservoirs, can evolve into four different steady states: thermal, thermal-like, quantum memory and oscillating quantum memory states. The first two steady states \textit{de facto} provided a rigorous proof how the system relaxes to thermal equilibrium with its environment. The latter two steady states, with strong non-Markovian effects, will maintain the initial state information and not reach thermal equilibrium, which is beyond the conventional wisdom of statistical mechanics.

5 pages, 3 figures

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• Uncovering nonperturbative dynamics of the biased sub-Ohmic spin-boson model with variational Matrix Product States
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• Open-system eigenstate thermalization in a noninteracting integrable model
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• Transitional steady states of exchange dynamics between finite quantum systems
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