General solution of the three-site master equation and the discrete Riccati equation

Details General solution of the three-site master equation and the discrete Riccati equation General solution of the three-site master equation and the discrete Riccati equation

1997-06-18

arxiv.org/abs/cond-mat/9706193v2

Nuovo Cimento B 114 (June 1999) 717-722

Physics

Condensed Matter

Statistical Mechanics

5pp, no figs; based on a talk at the UIC workshop on integrable models and supersymmetry (June 12-14/97) by author Rosu

Scientific paper

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

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