Sunday, July 21, 2013

0912.4052 (Luciano Silvestri et al.)

Markovian relaxation and eigenstate-thermalization from an exact
simulation of a finite bath

Luciano Silvestri, Kurt Jacobs, Vanja Dunjko, Maxim Olshanii
Closed many-body quantum systems thermalize, even though they are described by the reversible evolution of quantum mechanics. They also act as thermal baths for small systems that are weakly coupled to them, inducing damping and thermalization. Here we exactly simulate this thermalization for an arbitrary small system at a given temperature, T, by using a finite bath. This is achieved by giving the bath the appropriate key properties: the correct distribution of energy levels (as determined by statistical mechanics), and the property of typicality, obtained using a randomized coupling operator. Our motivations are i) to obtain thermalization from unitary evolution using a model in which the bath has known fundamental properties of many-body systems, ii) to explore the minimal numerical resources necessary to accurately simulate thermalization, iii) to show that the mechanism for relaxation in this model is that of eigenstate thermalization, and iv) to confirm that for weak damping the model agrees quantitatively with Fermi's golden rule, and thus with the dynamics of the Markovian Redfield master equation. We also discuss the question of whether, and when, the relaxation dynamics of systems coupled to thermal baths is universal, and what models might correctly reproduce it.
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