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Updated: Sep 8, 2025

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Long-term properties of finite-correlation-time isotropic stochastic systems
A S Il'yn1, A V Kopyev1, V A Sirota1
1P. N. Lebedev Physical Institute, RAS, Leninskij Prospekt 53, 119991 Moscow, Russia.
Abstract:
We consider finite-dimensional systems of linear stochastic differential equations ∂_{t}x_{k}(t)=A_{kp}(t)x_{p}(t), A(t) being a stationary continuous statistically isotropic stochastic process with values in real d×d matrices. We suppose that the laws of A(t) satisfy the large-deviation principle. For these systems, we find exact expressions for the Lyapunov and generalized Lyapunov exponents and show that they are determined in a precise way only by the rate function of the diagonal elements of A.
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