Random transition-rate matrices for the master equation

Details Random transition-rate matrices for the master equation Random transition-rate matrices for the master equation

2009-05-18

arxiv.org/abs/0905.2859v2

Physics

Condensed Matter

Statistical Mechanics

15 pages, 12 figures

Scientific paper

Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of independent rates of forward and backward transitions are considered. The first case leads to symmetric transition-rate matrices, whereas the second corresponds to general, asymmetric matrices. The resulting matrix ensembles are different from the standard ensembles and show different eigenvalue distributions. For example, the fraction of real eigenvalues scales anomalously with matrix dimension in the asymmetric case.

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