HAL CCSD
An investigation of equilibration in small quantum systems: the example of a particle in a 1D random potential
Luck, J M
Institut de Physique Théorique - UMR CNRS 3681 (IPHT) ; Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)
19 pages, 7 figures, 1 table
International audience
ISSN: 1751-8113
EISSN: 1751-8121
Journal of Physics A: Mathematical and Theoretical
IOP Publishing
cea-01485001
https://cea.hal.science/cea-01485001
https://cea.hal.science/cea-01485001
Journal of Physics A: Mathematical and Theoretical, 2016, 49 (11503), ⟨10.1088/1751-8113/49/11/115303⟩
ARXIV: 1510.06163
info:eu-repo/semantics/altIdentifier/arxiv/1510.06163
DOI: 10.1088/1751-8113/49/11/115303
info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/49/11/115303
en
[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]
info:eu-repo/semantics/article
Journal articles
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