Diverging fluctuations of the Lyapunov exponents

Diego Pazo; Juan M. Lopez; Antonio Politi

doi:10.1103/PhysRevLett.117.034101

Diverging fluctuations of the Lyapunov exponents

Diego Pazo, Juan M. Lopez, Antonio Politi

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Abstract

We show that in generic one-dimensional Hamiltonian lattices the diffusion coefficient of the maximum Lyapunov exponent diverges in the thermodynamic limit. We trace this back to the long-range correlations associated with the evolution of the hydrodynamic modes. In the case of normal heat transport, the divergence is even stronger, leading to the breakdown of the usual single-function Family-Vicsek scaling ansatz. A similar scenario is expected to arise in the evolution of rough interfaces in the presence of a suitably correlated background noise.

Original language	English
Article number	034101
Pages (from-to)	1-5
Number of pages	5
Journal	Physical Review Letters
Volume	117
Issue number	3
DOIs	https://doi.org/10.1103/PhysRevLett.117.034101
Publication status	Published - 14 Jul 2016

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Diverging Fluctuations of the Lyapunov Exponents
Final published version available at: https://doi.org/10.1103/PhysRevLett.117.034101 © 2016 American Physical Society https://journals.aps.org/authors/transfer-of-copyright-agreement
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Cite this

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abstract = "We show that in generic one-dimensional Hamiltonian lattices the diffusion coefficient of the maximum Lyapunov exponent diverges in the thermodynamic limit. We trace this back to the long-range correlations associated with the evolution of the hydrodynamic modes. In the case of normal heat transport, the divergence is even stronger, leading to the breakdown of the usual single-function Family-Vicsek scaling ansatz. A similar scenario is expected to arise in the evolution of rough interfaces in the presence of a suitably correlated background noise.",

author = "Diego Pazo and Lopez, {Juan M.} and Antonio Politi",

note = "D. P. acknowledges support by MINECO (Spain) under a Ram{\'o}n y Cajal fellowship. We acknowledge support by MINECO (Spain) under Project No. FIS2014-59462-P.",

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N2 - We show that in generic one-dimensional Hamiltonian lattices the diffusion coefficient of the maximum Lyapunov exponent diverges in the thermodynamic limit. We trace this back to the long-range correlations associated with the evolution of the hydrodynamic modes. In the case of normal heat transport, the divergence is even stronger, leading to the breakdown of the usual single-function Family-Vicsek scaling ansatz. A similar scenario is expected to arise in the evolution of rough interfaces in the presence of a suitably correlated background noise.

AB - We show that in generic one-dimensional Hamiltonian lattices the diffusion coefficient of the maximum Lyapunov exponent diverges in the thermodynamic limit. We trace this back to the long-range correlations associated with the evolution of the hydrodynamic modes. In the case of normal heat transport, the divergence is even stronger, leading to the breakdown of the usual single-function Family-Vicsek scaling ansatz. A similar scenario is expected to arise in the evolution of rough interfaces in the presence of a suitably correlated background noise.

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Diverging fluctuations of the Lyapunov exponents

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