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...

Full description

Saved in:
Bibliographic Details
Published inJournal of statistical physics Vol. 163; no. 4; pp. 765 - 783
Main Authors Il’yn, A. S., Sirota, V. A., Zybin, K. P.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.05.2016
Springer
Subjects
Differential equations
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Stochastic equations
Random matrices
T-exponential
Turbulence
Lyapunov exponents
Functional integral
Online AccessGet full text

Cover

More Information
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