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Related papers: Equilibration of Quasi-Integrable Systems

200 papers

The integrable nonlinear Schr\"odinger equation (NLSE) is a fundamental model of nonlinear science which also has important consequences in engineering. The powerful framework of the periodic inverse scattering transform (IST) provides a…

Signal Processing · Electrical Eng. & Systems 2019-11-28 Jan-Willem Goossens , Hartmut Hafermann , Yves Jaouën

We study the equilibrium time correlations for the conserved fields of classical anharmonic chains and argue that their dynamic correlator can be predicted on the basis of nonlinear fluctuating hydrodynamics. In fact our scheme is more…

Statistical Mechanics · Physics 2013-12-10 Christian B. Mendl , Herbert Spohn

It is commonly assumed that a large system, weakly coupled to a thermal environment through its boundaries, relaxes quasistatically towards the new equilibrium even when the temperature of the environment changes abruptly. Here we show how…

Statistical Mechanics · Physics 2024-11-21 Ran Yaacoby , Oren Raz , Gianluca Teza

We study a certain type of the celebrated Fermi-Pasta-Ulam particle chain, namely the inverted FPU model, where the inter-particle potential has a form of a quartic double well. Numerical evidence is given in support of a simple symbolic…

Chaotic Dynamics · Physics 2009-10-31 Marko Znidaric , Tomaz Prosen

The relaxation to equilibrium in many systems which show strange kinetics is described by fractional Fokker-Planck equations (FFPEs). These can be considered as phenomenological equations of linear nonequilibrium theory. We show that the…

Statistical Mechanics · Physics 2009-11-07 I. M. Sokolov

The non-equilibrium dynamics of integrable systems are special: there is substantial evidence that after a quantum quench they do not thermalize but their asymptotic steady state can be described by a Generalized Gibbs Ensemble (GGE). Most…

Statistical Mechanics · Physics 2013-11-27 Marton Kormos , Aditya Shashi , Yang-Zhi Chou , Jean-Sebastien Caux , Adilet Imambekov

Correlated classical and quantum many-particle systems out of equilibrium are of high interest in many fields, including dense plasmas, correlated solids, and ultracold atoms. Accurate theoretical description of these systems is challenging…

Statistical Mechanics · Physics 2026-04-02 Erik Schroedter , Michael Bonitz

Integrable systems offer rare examples of solvable many-body problems in the quantum world. Due to the fine-tuned structure, their realization in nature and experiment is never completely accurate, therefore effects of integrability are…

Statistical Mechanics · Physics 2024-07-24 Iris Ulčakar , Zala Lenarčič

In this paper, we develop and analyze an integral fixed-time sliding mode control method for a scenario in which the system model is only partially known, utilizing Gaussian processes. We present two theorems on fixed-time convergence. The…

Systems and Control · Electrical Eng. & Systems 2025-05-30 Chaimae El Mortajinea , Moussa Labbadib , Adnane Saoudc , Mostafa Bouzia

We study theoretically phonon-assisted relaxation processes in a system consisting of one or two electrons confined in two vertically stacked self-assembled quantum dots. The calculation is based on a k.p approximation for single particle…

Mesoscale and Nanoscale Physics · Physics 2010-09-14 Krzysztof Gawarecki , Michał Pochwała , Anna Grodecka-Grad , Paweł Machnikowski

We consider a version of the classical Hamiltonian FPU (Fermi-Pasta-Ulam) problem with nonlinear force-strain relation in which a hardening response is taken over by a softening regime above a critical strain value. We show that in addition…

Pattern Formation and Solitons · Physics 2024-04-25 Anna Vainchtein , Lev Truskinovsky

Recent numerical results showed that thermalization of Fourier modes is achieved in short time-scales in the Toda model, despite its integrability and the absence of chaos. Here we provide numerical evidence that the scenario according to…

Statistical Mechanics · Physics 2022-06-22 Niccolò Cocciaglia , Angelo Vulpiani , Giacomo Gradenigo

We investigate the connection between local and global dynamics of two N-degree of freedom Hamiltonian systems with different origins describing one-dimensional nonlinear lattices: The Fermi-Pasta-Ulam (FPU) model and a discretized version…

Chaotic Dynamics · Physics 2016-12-21 Chris Antonopoulos , Tassos Bountis , Charalampos Skokos

We study the dynamics of the $(\alpha+\beta)$ Fermi-Pasta-Ulam-Tsingou lattice (FPUT lattice, for short) for an arbitrary number $N$ of interacting particles, in regimes of small enough nonlinearity so that a Birkhoff-Gustavson type of…

Chaotic Dynamics · Physics 2025-03-03 Tiziana Comito , Matteo Lotriglia , Miguel D. Bustamante

We revisit an algorithm constructing elliptic tori, that was originally designed for applications to planetary hamiltonian systems. The scheme is adapted to properly work with models of chains of $N+1$ particles interacting via anharmonic…

Mathematical Physics · Physics 2021-02-26 Chiara Caracciolo , Ugo Locatelli

In these lecture notes, we present, contextualize, and discuss the phenomenon of metastability (or prethermalization) in the Fermi-Pasta-Ulam-Tsingou lattice and similar models from the viewpoint of perturbation theory. We provide an…

Mathematical Physics · Physics 2025-09-23 Matteo Gallone

We perform a stochastic model reduction of the Kuramoto-Sakaguchi model for finitely many coupled phase oscillators with phase frustration. Whereas in the thermodynamic limit coupled oscillators exhibit stationary states and a constant…

Adaptation and Self-Organizing Systems · Physics 2024-05-14 Wenqi Yue , Georg A. Gottwald

Molecular dynamics simulations of a quasi-harmonic solid are conducted to elucidate the meaning of temperature fluctuations in canonical systems and validate a well-known but frequently contested equation predicting the mean square of such…

Statistical Mechanics · Physics 2016-12-01 J. Hickman , Y. Mishin

We study the out-of-equilibrium dynamics of entanglement fluctuations in the $\nu=1$ Quantum Symmetric Simple Exclusion Process, a free-fermion chain with hopping amplitudes that are stochastic in time but homogeneous in space. Previous…

Statistical Mechanics · Physics 2026-05-11 Angelo Russotto , Filiberto Ares , Pasquale Calabrese , Vincenzo Alba

This review provides an up-to-date account of energy transport in Fermi-Pasta-Ulam-Tsingou (FPUT) chains, a key testbed for nonequilibrium statistical physics. We discuss the transition from the historical puzzle of thermalization to the…

Statistical Mechanics · Physics 2026-02-18 Stefano Lepri , Roberto Livi , Antonio Politi