Article Dans Une Revue Physical Review E : Statistical, Nonlinear, and Soft Matter Physics [2001-2015] Année : 1996

Sample-size dependence of the ground-state energy in a one-dimensional localization problem

Résumé

We study the sample-size dependence of the ground-state energy in a one-dimensional localization problem, based on a supersymmetric quantum mechanical Hamiltonian with random Gaussian potential. We determine, in the form of bounds, the precise form of this dependence and show that the disorder-average ground-state energy decreases with an increase of the size $R$ of the sample as a stretched-exponential function, $\\exp( - R^{z})$, where the characteristic exponent $z$ depends merely on the nature of correlations in the random potential. In the particular case where the potential is distributed as a Gaussian white noise we prove that $z = 1/3$. We also predict the value of $z$ in the general case of Gaussian random potentials with correlations.

Dates et versions

hal-00004278 , version 1 (17-02-2005)

Identifiants

Citer

C. Monthus, G. Oshanin, A. Comtet, S. F. Burlatsky. Sample-size dependence of the ground-state energy in a one-dimensional localization problem. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics [2001-2015], 1996, 54, pp.231. ⟨hal-00004278⟩
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