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arXiv · 1110.1270

Quantum chaos and effective thermalization

Alexander Altland·Fritz Haake
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Abstract

We demonstrate effective equilibration for unitary quantum dynamics under conditions of classical chaos. Focusing on the paradigmatic example of the Dicke model, we show how a constructive description of the thermalization process is facilitated by the Glauber $Q$ or Husimi function, for which the evolution equation turns out to be of Fokker-Planck type. The equation describes a competition of classical drift and quantum diffusion in contractive and expansive directions. By this mechanism the system follows a 'quantum smoothened' approach to equilibrium, which avoids the notorious singularities inherent to classical chaotic flows.

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Alexander Altland, Fritz Haake. 2012-03-21. Quantum chaos and effective thermalization. https://doi.org/10.1103/physrevlett.108.073601

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