Equilibration of quantum chaotic systems

Abstract

Quantum ergordic theorem for a large class of quantum systems was proved by von Neumann [Z. Phys. {\bf 57}, 30 (1929)] and again by Reimann [Phys. Rev. Lett. {\bf 101}, 190403 (2008)] in a more practical and well-defined form. However, it is not clear whether the theorem applies to quantum chaotic systems. With the rigorous proof still elusive, we illustrate and verify this theorem for quantum chaotic systems with examples. Our numerical results show that a quantum chaotic system with an initial low-entropy state will dynamically relax to a high-entropy state and reach equilibrium. The quantum equilibrium state reached after dynamical relaxation bears a remarkable resemblance to the classical micro-canonical ensemble. However, the fluctuations around equilibrium are distinct: the quantum fluctuations are exponential while the classical fluctuations are Gaussian.

11 pages, 8 figures

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• Entropy for Quantum Pure States and Its Dynamical Relaxation
• Quantum non-stationary phenomena of spin systems in collision models
• Statistically preferred basis of an open quantum system: Its relation to the eigenbasis of a renormalized self-Hamiltonian
• Observation of Quantum Equilibration in Dilute Bose Gases
• Roles of energy eigenstates and eigenvalues in equilibration of isolated quantum systems
• Equilibration of Non-interacting Photons and Quantum Signatures of Chaos