An investigation of equilibration in small quantum systems: the example of a particle in a 1D random potential. (2nd February 2016)

• Record Type: Journal Article
• Authors: Luck, J M
• Is Part Of: Journal of physics. Volume 49:Number 11(2016)
• Publication Date: 2016-02-02
• Subjects: equilibration -- localization -- quantum mechanics -- quantum walks; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/49/11/115303
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: 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.