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Lyapunov exponent and susceptibility

dc.contributor.author Charbonneau, Patrick
dc.contributor.author Li, Y
dc.contributor.author Pfister, HD
dc.contributor.author Yaida, Sho
dc.date.accessioned 2017-08-23T16:05:28Z
dc.date.available 2017-08-23T16:05:28Z
dc.date.issued 2017-08-23
dc.identifier http://arxiv.org/abs/1707.00708v1
dc.identifier.uri http://hdl.handle.net/10161/15347
dc.description.abstract 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.
dc.format.extent 9 pages, 4 figures
dc.subject cond-mat.stat-mech
dc.subject cond-mat.stat-mech
dc.title Lyapunov exponent and susceptibility
dc.type Journal article
pubs.author-url http://arxiv.org/abs/1707.00708v1
pubs.organisational-group Chemistry
pubs.organisational-group Duke
pubs.organisational-group Physics
pubs.organisational-group Trinity College of Arts & Sciences


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