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

Abstract

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.

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

References in corpus (3)

• Localization Properties in One Dimensional Disordered Supersymmetric Quantum Mechanics
• Thermal Equilibrium with the Wiener Potential: Testing the Replica Variational Approximation
• DIFFUSIVE TRANSPORT IN A ONE DIMENSIONAL DISORDERED POTENTIAL INVOLVING CORRELATIONS

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