Journal of Statistical Physics, Vol. 103, Nos. 34, 2001, p. 575-588.
A path-integral method is extended and developed to investigate the statistical
physics of one-dimensional random systems. Evaluation of the one-particle
partition function and density matrix is simplified to finding a solution for a
second-order ordinary differential equation. This makes it possible to obtain
analytic solutions or conduct accurate numerical calculations for the random
systems. With this approach, an analytical solution for the Gaussian model is
obtained and the statistical physics of the FrischLloyd model is studied.