Berlin 2018 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 12: Dynamics in Many-Body Systems: Interference, Equilibration and Localization I (joint session DY/TT)

TT 12.6: Vortrag

Montag, 12. März 2018, 11:30–11:45, EB 107

Non-Ergodic Dynamics in Many-Body Systems — Carlo Danieli and •Sergej Flach — Center for Theoretical Physics of Complex Systems, Institute for Basic Sciences, Daejeon, Korea

Integrable models are characterized by a set of preserved actions. Close to the limits, the nonintegrable perturbations span a coupling network in action space which can be short or long ranged. The equilibrium dynamics of a system close to such limits is sensitive to the network type. Long range networks enforce ergodicity with large but finite relaxation time scales at a finite distance to the integrable limit. Short range networks lead to a loss of ergodicity at a finite distance from the limit. We demonstrate this by choosing observables which turn conserved actions at the limit. Off the limit, and fixing their value to the proper statistical average, they define manifolds in the phase space of an ergodic and equipartitioned many-body system. A typical trajectory pierces such manifolds infinitely often as time goes to infinity. Close to the integrable limit, the dynamics yields a power-law distribution of the excursion times off the manifolds. The exponent is used as a measure of distance from a potential nonergodic regime. We analyse several cases: the Fermi Pasta Ulam chain in the limit of small energies (long range network), and the Klein-Gordon, Discrete Gross Pitaevskii and coupled rotor lattices in the limit of large energies (short range network).