C. Monthus 1, G. Oshanin 2, A. Comtet 2, 3, S. F. Burlatsky 4
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 54 (1996) 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.
- 1. Service de Physique Théorique (SPhT),
CNRS : URA2306 – CEA : DSM/SPHT - 2. Division de Physique Théorique, IPN,
Université Paris XI – Paris Sud - 3. LPTPE,
Université Paris VI – Pierre et Marie Curie - 4. Department of Chemistry, BG-10,
University of Washington