Abstract
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 Frisch–Lloyd model is studied.
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