General solution of the three-site master equation and the discrete Riccati equation
Statistical Mechanics
2008-02-03 v2 Mathematical Physics
math.MP
Abstract
We first obtain by analogy with the continuous (differential) case the general solution of a discrete Riccati equation. Our results can be considered the discrete analog of Mielnik's construction in supersymmetric quantum mechanics [J. Math. Phys. 25, 3387 (1984)]. Moreover, we establish the full equivalence between our discrete Riccati equation and a corresponding homogeneous second order discrete linear equation. We present an application to the three-site master equation obtaining explicitly the general solutions for the simple cases of free random walk and the biased random walk
Keywords
Cite
@article{arxiv.cond-mat/9706193,
title = {General solution of the three-site master equation and the discrete Riccati equation},
author = {M. A. Reyes and H. C. Rosu},
journal= {arXiv preprint arXiv:cond-mat/9706193},
year = {2008}
}
Comments
5pp, no figs; based on a talk at the UIC workshop on integrable models and supersymmetry (June 12-14/97) by author Rosu