%0 Journal Article
%T An investigation of equilibration in small quantum systems: the example of a particle in a 1D random potential
%+ Institut de Physique ThÃ©orique - UMR CNRS 3681 (IPHT)
%A Luck, J M
%Z 19 pages, 7 figures, 1 table
%< avec comitÃ© de lecture
%Z t15/182
%@ 1751-8113
%J Journal of Physics A: Mathematical and Theoretical
%I IOP Publishing
%V 49
%N 11503
%8 2016-03-18
%D 2016
%Z 1510.06163
%R 10.1088/1751-8113/49/11/115303
%Z Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]Journal articles
%X We investigate the equilibration of a small isolated quantum system by means of its matrix of asymptotic transition probabilities in a preferential basis. The trace of this matrix is shown to measure the degree of equilibration of the system launched from a typical state, from the standpoint of the chosen basis. This approach is substantiated by an in-depth study of the example of a tight-binding particle in one dimension. In the regime of free ballistic propagation, the above trace saturates to a finite limit, testifying good equilibration. In the presence of a random potential, the trace grows linearly with the system size, testifying poor equilibration in the insulating regime induced by Anderson localization. In the weak-disorder situation of most interest, a universal finite-size scaling law describes the crossover between the ballistic and localized regimes. The associated crossover exponent 2/3 is dictated by the anomalous band-edge scaling characterizing the most localized energy eigenstates.
%G English
%L cea-01485001
%U https://cea.hal.science/cea-01485001
%~ CEA
%~ CNRS
%~ DSM-IPHT
%~ CEA-UPSAY
%~ UNIV-PARIS-SACLAY
%~ CEA-UPSAY-SACLAY
%~ CEA-DRF
%~ GS-MATHEMATIQUES
%~ GS-PHYSIQUE