Berlin 2018 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 15: Nonlinear Dynamics, Synchronization, Chaos I
DY 15.7: Talk
Monday, March 12, 2018, 17:00–17:15, BH-N 128
memory effects in the strongly anharmonic FPUT model — •Graziano Amati1, Hugues Meyer2, and Tanja Schilling1 — 1Physikalisches Institut, Albert-Ludwigs-Universität, 79104 Freiburg, Germany — 2Research Unit in Engineering Science, Université du Luxembourg, L-4364 Esch-sur-Alzette, Luxembourg
The Fermi-Pasta-Ulam-Tsingou (FPUT) Problem represents an intriguing challenge in Modern Physics. In its original formulation, it questions whether or not a Dynamical System can reach thermalization if a small anharmonicity is added to an integrable system, under specific out-of-equilibrium initial conditions. The problem was originally raised by the apparent lack of energy spreading between the normal modes of a one-dimensional chain of particles with a small anharmonicity, in case the energy at the initial time is given to the lowest frequencies of the system.
In the present work, we consider a one-dimensional chain of many particles with a strongly anharmonic interaction potential. The model is initialized at canonical equilibrium, and we take as a relevant variable the Fourier Transform of the density of particles for a tagged degree of freedom. The time correlation function of this observable exhibits an interesting non-ergodic behavior due to a temperature-driven ’FPU-like’ dynamical localization, that corresponds to a nontrivial memory profile.
Via a novel coarse-graining technique, we are able to reconstruct the dynamics of the memory, and to show that the exhibited non-ergodicity can be rephrased via the memory kernel of the process.