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

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

1995-12-21

arxiv.org/abs/cond-mat/9512170v1

Physics

Condensed Matter

30 pages and 4 figures (not included). The figures are available upon request

Scientific paper

10.1103/PhysRevE.54.231

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.

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