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Dyson's Brownian Motion and Universal Dynamics of Quantum Systems

Onuttom Narayan·B. Sriram Shastry
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Abstract

We establish a correspondence between the evolution of the distribution of eigenvalues of a $N\times N$ matrix subject to a random Gaussian perturbing matrix, and a Fokker-Planck equation postulated by Dyson. Within this model, we prove the equivalence conjectured by Altshuler et al between the space-time correlations of the Sutherland-Calogero-Moser system in the thermodynamic limit and a set of two-variable correlations for disordered quantum systems calculated by them. Multiple variable correlation functions are, however, shown to be inequivalent for the two cases.

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Onuttom Narayan, B. Sriram Shastry. 1993-06-10. Dyson's Brownian Motion and Universal Dynamics of Quantum Systems. https://doi.org/10.1103/physrevlett.71.2106

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