Article (Scientific journals)
Memory Effects in the Fermi–Pasta–Ulam Model
Amati, Graziano; Meyer, Hugues; Schilling, Tanja
2019In Journal of Statistical Physics, 174 (1), p. 219-257
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Keywords :
FPU Model; Coarse-graining; Generalized Langevin Equation
Abstract :
[en] We study the intermediate scattering function (ISF) of the strongly-nonlinear Fermi–Pasta–Ulam Model at thermal equilibrium, using both numerical and analytical methods. From the molecular dynamics simulations we distinguish two limit regimes, as the system behaves as an ideal gas at high temperature and as a harmonic chain for low excitations. At intermediate temperatures the ISF relaxes to equilibrium in a nontrivial fashion. We then calculate analytically the Taylor coefficients of the ISF to arbitrarily high orders (the specific, simple shape of the two-body interaction allows us to derive an iterative scheme for these). The results of the recursion are in good agreement with the numerical ones. Via an estimate of the complete series expansion of the scattering function, we can reconstruct within a certain temperature range its coarse-grained dynamics. This is governed by a memory-dependent Generalized Langevin Equation (GLE), which can be derived via projection operator techniques. Moreover, by analyzing the first series coefficients of the ISF, we can extract a parameter associated to the strength of the memory effects in the dynamics.
Disciplines :
Physics
Author, co-author :
Amati, Graziano;  Albert-Ludwigs-Universität Freiburg > Physikalisches Insitut
Meyer, Hugues ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Physics and Materials Science Research Unit ; Albert-Ludwigs-Universität Freiburg > Physikalisches Institut
Schilling, Tanja;  Albert-Ludwigs-Universität Freiburg > Physikalisches Institut
External co-authors :
yes
Language :
English
Title :
Memory Effects in the Fermi–Pasta–Ulam Model
Publication date :
15 January 2019
Journal title :
Journal of Statistical Physics
ISSN :
1572-9613
Publisher :
Kluwer Academic/Plenum Publishers, United States
Volume :
174
Issue :
1
Pages :
219-257
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Physics and Materials Science
Available on ORBilu :
since 10 April 2019

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