Lyapunov exponent and susceptibility

Charbonneau, Patrick

Li, Yue Cathy

Pfister, Henry D

Yaida, Sho

2017-08-23T16:05:28Z

2017-08-23T16:05:28Z

2017-08-23

Lyapunov exponents characterize the chaotic nature of dynamical systems by quantifying the growth rate of uncertainty associated with imperfect measurement of the initial conditions. Finite-time estimates of the exponent, however, experience fluctuations due to both the initial condition and the stochastic nature of the dynamical path. The scale of these fluctuations is governed by the Lyapunov susceptibility, the finiteness of which typically provides a sufficient condition for the law of large numbers to apply. Here, we obtain a formally exact expression for this susceptibility in terms of the Ruelle dynamical zeta function. We further show that, for systems governed by sequences of random matrices, the cycle expansion of the zeta function enables systematic computations of the Lyapunov susceptibility and of its higher-moment generalizations. The method is here applied to a class of dynamical models that maps to static disordered spin chains with interactions stretching over a varying distance, and is tested against Monte Carlo simulations.

9 pages, 4 figures

http://arxiv.org/abs/1707.00708v1

https://hdl.handle.net/10161/15347

American Physical Society (APS)

cond-mat.stat-mech

cond-mat.stat-mech

Lyapunov exponent and susceptibility

Journal article

Charbonneau, Patrick|0000-0001-7174-0821

Pfister, Henry D|0000-0001-5521-4397

http://arxiv.org/abs/1707.00708v1

Chemistry

Duke

Physics

Trinity College of Arts & Sciences