Preferred basis derived from eigenstate thermalization hypothesis

• URL: http://arxiv.org/abs/2201.06308v2
• Date: Tue, 25 Oct 2022 16:00:56 GMT
• Title: Preferred basis derived from eigenstate thermalization hypothesis
• Authors: Hua Yan, Jiaozi Wang, and Wen-ge Wang
• Abstract summary: We study the long-time average of the reduced density matrix (RDM) of an $m$-level central 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.
• Score: 1.7606558873844536
• License: http://creativecommons.org/licenses/by/4.0/
• 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 Schr\"{o}dinger 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.

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