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arXiv · 1311.1282

Non-Markovian Dynamics Impact on the Foundations of Statistical Mechanics

Heng-Na Xiong·Ping-Yuan Lo·Wei-Min Zhang·Franco Nori·Da Hsuan Feng
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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.

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Heng-Na Xiong, Ping-Yuan Lo, Wei-Min Zhang, Franco Nori, Da Hsuan Feng. 2013-11-06. Non-Markovian Dynamics Impact on the Foundations of Statistical Mechanics. https://doi.org/10.1038/srep13353

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