Preferred basis derived from eigenstate thermalization hypothesis

Abstract

We study the long-time average of the reduced density matrix (RDM) of an $m$-level central system, which is locally coupled to a large environment, under an overall Schrödinger evolution of the total system. We consider a class of interaction Hamiltonian, whose environmental part satisfies the so-called eigenstate thermalization hypothesis (ETH) ansatz with a constant diagonal part in the energy region concerned. On the eigenbasis of the central system's Hamiltonian, $\frac{1}{2}(m-1)(m+2)$ relations among elements of the averaged RDM are derived. When steady states exist, these relations imply the existence of a preferred basis, given by a renormalized Hamiltonian that includes certain averaged impact of the system-environment interaction. Numerical simulations performed for a qubit coupled to a defect Ising chain conform the analytical predictions.

References in corpus (10)

• Thermalization and its mechanism for generic isolated quantum systems
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Anomalous thermalization in ergodic systems
• Decoherence in adiabatic quantum computation
• Universality in the onset of quantum chaos in many-body systems
• Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain
• Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
• Non-Canonical Statistics of a Spin-Boson Model: Theory and Exact Monte-Carlo Simulations
• Entanglement-induced Decoherence and Energy Eigenstates
• A decoherence interpretation of quantum work for adiabatic processes