%0 Unpublished work
%T Equilibration properties of small quantum systems: further examples
%+ Institut de Physique ThÃ©orique - UMR CNRS 3681 (IPHT)
%A Luck, J. M.
%Z 30 pages, 8 figures, 3 tables
%Z t17/021
%8 2017-03-07
%D 2017
%Z 1702.05909
%Z Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]Preprints, Working Papers, ...
%X It has been proposed to investigate the equilibration properties of a small isolated quantum system by means of the matrix of asymptotic transition probabilities in some preferential basis. The trace $T$ of this matrix measures the degree of equilibration of the system prepared in a typical state of the preferential basis. This quantity may vary between unity (ideal equilibration) and the dimension $N$ of the Hilbert space (no equilibration at all). Here we analyze several examples of simple systems where the behavior of $T$ can be investigated by analytical means. We first study the statistics of $T$ when the Hamiltonian governing the dynamics is random and drawn from a distribution invariant under the group U$(N)$ or O$(N)$. We then investigate a quantum spin $S$ in a tilted magnetic field making an arbitrary angle with the preferred quantization axis, as well as a tight-binding particle on a finite electrified chain. The last two cases provide examples of the interesting situation where varying a system parameter -- such as the tilt angle or the electric field -- through some scaling regime induces a continuous transition from good to bad equilibration properties.
%G English
%2 https://cea.hal.science/cea-01484658/document
%2 https://cea.hal.science/cea-01484658/file/1702.05909.pdf
%L cea-01484658
%U https://cea.hal.science/cea-01484658
%~ CEA
%~ CNRS
%~ DSM-IPHT
%~ CEA-UPSAY
%~ UNIV-PARIS-SACLAY
%~ CEA-UPSAY-SACLAY
%~ CEA-DRF
%~ TEST-HALCNRS
%~ GS-MATHEMATIQUES
%~ GS-PHYSIQUE