%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 Théorique - UMR CNRS 3681 (IPHT) %A Luck, J M %Z 19 pages, 7 figures, 1 table %< avec comité 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