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Lyapunov exponent and rotation number for stochastic Dirac operators

Lyapunov exponent and rotation number for stochastic Dirac operators In this paper, we consider the stochastic Dirac operator $$L_\omega = \left( {\begin{array}{*{20}c} 0{ - 1} \\ 10 \\ \end{array} } \right)\frac{d}{{dt}} - \left( {\begin{array}{*{20}c} {p(T_t \omega )}0 \\ { 0}{q(T_t \omega )} \\ \end{array} } \right)$$ on a polish space (Θ, β,P). The relation between the Lyapunov index, rotation number and the spectrum ofL ω is discussed. The existence of the Lyapunov index and rotation number is shown. By using the W-T functions and W-function we prove the theorems forL ω as in Kotani [1], [2] for Schrödinger operators, and in Johnson [5] for Dirac operators on compact space. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Lyapunov exponent and rotation number for stochastic Dirac operators

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Publisher
Springer Journals
Copyright
Copyright © 1992 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02006742
Publisher site
See Article on Publisher Site

Abstract

In this paper, we consider the stochastic Dirac operator $$L_\omega = \left( {\begin{array}{*{20}c} 0{ - 1} \\ 10 \\ \end{array} } \right)\frac{d}{{dt}} - \left( {\begin{array}{*{20}c} {p(T_t \omega )}0 \\ { 0}{q(T_t \omega )} \\ \end{array} } \right)$$ on a polish space (Θ, β,P). The relation between the Lyapunov index, rotation number and the spectrum ofL ω is discussed. The existence of the Lyapunov index and rotation number is shown. By using the W-T functions and W-function we prove the theorems forL ω as in Kotani [1], [2] for Schrödinger operators, and in Johnson [5] for Dirac operators on compact space.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

References