Berlin 2018 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 40: Dual-Method Approaches to Quantum Many-Body Systems II

TT 40.5: Vortrag

Dienstag, 13. März 2018, 11:00–11:15, H 3010

Microscopical justification of the eigenstate thermalization hypothesis (ETH) — •Nils O. Abeling and Stefan Kehrein — Institut für Theoretische Physik, Fakultät für Physik, Georg-August-Universität Göttingen

The ETH postulates how isolated quantum many-body systems thermalize. It is essential to the understanding of thermalization and implicates various thermodynamic relations [1]. While there are several numerical verifications of the ETH ([2]), only few analytical arguments have been found so far. They, in particular, are based on semiclassical approaches [3]. Another argument was given by J. Deutsch who showed how a small interaction which is modelled by a random matrix leads to thermalization [4]. Our work adopts this idea and analyzes whether and how a generic quantum system can be treated as a random matrix. To do this we employ the flow equation method that performs continuous unitary transformations to map an initial Hamiltonian to an effective Hamiltonian. The latter takes on a banded form and is compared to a random matrix. By studying the statistical properties of the numerically obtained matrices we are able to use the analytical flow equation approach to close the gap in Deutsch’s reasoning. Our results depict the first step towards a microscopic justification of the eigenstate thermalization hypothesis.
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