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An investigation of equilibration in small quantum systems: the example of a particle in a 1D random potential

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.
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Contributor : Emmanuelle de Laborderie <>
Submitted on : Wednesday, March 8, 2017 - 9:56:16 AM
Last modification on : Monday, June 15, 2020 - 2:52:03 PM

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J M Luck. An investigation of equilibration in small quantum systems: the example of a particle in a 1D random potential. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2016, 49 (11503), ⟨10.1088/1751-8113/49/11/115303⟩. ⟨cea-01485001⟩

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