cea-01485001
https://cea.hal.science/cea-01485001
arxiv:1510.06163
doi:10.1088/1751-8113/49/11/115303
[CEA] CEA - Commissariat à l'énergie atomique
[CNRS] CNRS - Centre national de la recherche scientifique
[DSM-IPHT] IPHT
[CEA-UPSAY] CEA - Université Paris-Saclay
[UNIV-PARIS-SACLAY] Université Paris-Saclay
[CEA-UPSAY-SACLAY] CEA-UPSAY-SACLAY
[CEA-DRF] Direction de Recherche Fondamentale
[GS-MATHEMATIQUES] Graduate School Mathématiques
[GS-PHYSIQUE] Graduate School Physique
An investigation of equilibration in small quantum systems: the example of a particle in a 1D random potential
Luck, J M
[PHYS.COND.CM-SM] Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]
ART
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.
2016-03-18
en
Journal of Physics A: Mathematical and Theoretical
IOP Publishing