Volume 121, Number 4, February 2018
|Number of page(s)||7|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||17 April 2018|
Thermalization in the discrete nonlinear Klein-Gordon chain in the wave-turbulence framework
1 Dipartimento di Fisica, Università degli Studi di Torino - Via P. Giuria, 1, Torino, 10125, Italy
2 INFN, Sezione di Torino - Via P. Giuria, 1, Torino, 10125, Italy
3 Sorbonne Université, CNRS, Institut Jean Le Rond d'Alembert - F-75005 Paris, France
Received: 15 January 2018
Accepted: 26 March 2018
We study the time of equipartition, Teq, of energy in the one-dimensional Discrete Nonlinear Klein-Gordon (DNKG) equation in the framework of the Wave Turbulence (WT) theory. We discuss the applicability of the WT theory and show how this approach can explain qualitatively the route to thermalization and the scaling of the equipartition time as a function of the nonlinear parameter ϵ, defined as the ratio between the nonlinear and linear part of the Hamiltonian. Two scaling laws, and , for different degrees of nonlinearity are explained in terms of four-wave or six-wave processes in the WT theory. The predictions are verified with extensive numerical simulations varying the system size and the degree of nonlinearity.
PACS: 47.52.+j – Chaos in fluid dynamics
© EPLA, 2018
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