Statistical Properties of the T-Exponential of Isotropically Distributed Random Matrices

A functional method for calculating averages of the time-ordered exponential of a continuous isotropic random N × N matrix process is presented. The process is not assumed to be Gaussian. In particular, the Lyapunov exponents and higher correlation functions of the T-exponent are derived from the st...

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Bibliographic Details
Published in:Journal of statistical physics 2016-05, Vol.163 (4), p.765-783
Main Authors: Il’yn, A. S., Sirota, V. A., Zybin, K. P.
Format: Article
Language:English
Subjects:
Differential equations
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Summary:A functional method for calculating averages of the time-ordered exponential of a continuous isotropic random N × N matrix process is presented. The process is not assumed to be Gaussian. In particular, the Lyapunov exponents and higher correlation functions of the T-exponent are derived from the statistical properties of the process. The approach may be of use in a wide range of physical problems. For example, in theory of turbulence the account of non-gaussian statistics is very important since the non-Gaussian behavior is responsible for the time asymmetry of the energy flow.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-016-1502-3