Statistically preferred basis of an open quantum system: Its relation to the eigenbasis of a renormalized self-Hamiltonian

Abstract

We study the problem of the basis of an open quantum system, under a quantum chaotic environment, which is preferred in view of its stationary reduced density matrix (RDM), that is, the basis in which the stationary RDM is diagonal. It is shown that, under an initial condition composed of sufficiently many energy eigenstates of the total system, such a basis is given by the eigenbasis of a renormalized self-Hamiltonian of the system, in the limit of large Hilbert space of the environment. Here, the renormalized self-Hamiltonian is given by the unperturbed self-Hamiltonian plus a certain average of the interaction Hamiltonian over the environmental degrees of freedom. Numerical simulations, performed in two models, both with the kicked rotor as the environment, give results consistent with the above analytical predictions for the limit of large environment.

11 pages, 9 figures

References in corpus (7)

• Thermalization and its mechanism for generic isolated quantum systems
• Non-Canonical Statistics of a Spin-Boson Model: Theory and Exact Monte-Carlo Simulations
• Conservative chaotic map as a model of quantum many-body environment
• Entanglement-induced Decoherence and Energy Eigenstates
• Eigenvalue statistics as indicator of integrability of non-equilibrium density operators
• Eigenvalue statistics of reduced density matrix during driving and relaxation
• Equilibration of quantum chaotic systems

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