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Related papers: q-Breathers and the Fermi-Pasta-Ulam Problem

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We study the inhomogeneous kinetic Fermi-Pasta-Ulam (FPU) equation, a nonlinear transport equation describing the evolution of phonon density distributions with four-phonon interactions. The equation combines free transport in physical…

Analysis of PDEs · Mathematics 2025-12-25 Haoling Xiang

Recent work has developed a nonlinear hydrodynamic fluctuation theory for a chain of coupled anharmonic oscillators governing the conserved fields, namely stretch, momentum, and energy. The linear theory yields two propagating sound modes…

Statistical Mechanics · Physics 2014-07-30 Suman G. Das , Abhishek Dhar , Keiji Saito , Christian B. Mendl , Herbert Spohn

The Fermi--Pasta--Ulam--Tsingou (FPUT) system, describing the evolution of $N$ coupled harmonic oscillators, has been the subject of much attention since the 1950's when experiments which contradicted predictions of thermalization of the…

Analysis of PDEs · Mathematics 2026-05-20 Katja Vassilev , Boyang Wu

We consider four masses in a circular configuration with nearest-neighbour interaction, generalizing the spatially periodic Fermi--Pasta--Ulam-chain where all masses are equal. We identify the mass ratios that produce the…

Chaotic Dynamics · Physics 2020-02-05 Heinz Hanßmann , Reza Mazrooei-Sebdani , Ferdinand Verhulst

Dynamics of the Fermi-Pasta-Ulam (FPU) system on a two-dimensional square lattice is considered in the limit of small-amplitude long-scale waves with slow transverse modulations. In the absence of transverse modulations, dynamics of such…

Analysis of PDEs · Mathematics 2022-09-28 Nikolay Hristov , Dmitry E. Pelinovsky

We show that, in the pure-quartic systems, modulation instability (MI) undergoes heteroclinic-structure transitions (HSTs) at two critical frequencies of {\omega} c1 and {\omega} c2 ( {\omega} c2 > {\omega} c1 ), which indicates that there…

Pattern Formation and Solitons · Physics 2022-05-03 Xiankun Yao , Chong Liu , Zhan-Ying Yang , Wen-Li Yang

Small-amplitude waves in the Fermi-Pasta-Ulam (FPU) lattice with weakly anharmonic interaction potentials are described by the generalized Korteweg-de Vries (KdV) equation. Justification of the small-amplitude approximation is usually…

Dynamical Systems · Mathematics 2016-03-07 Amjad Khan , Dmitry Pelinovsky

We consider a version of the classical Hamiltonian Fermi-Pasta-Ulam (FPU) problem with a trilinear force-strain relation of soft-hard-soft type that is in general non-symmetric. In addition to the classical spatially localized solitary…

Pattern Formation and Solitons · Physics 2024-06-11 Anna Vainchtein , Lev Truskinovsky

Quantum fluctuation of the energy is studied for an ultracold gas of interacting fermions trapped in a three-dimensional potential. Periodic-orbit theory is explored, and energy fluctuations are studied versus particle number for generic…

Atomic Physics · Physics 2009-11-13 M. Puig von Friesen , M. Ogren , S. Aberg

We study the interaction of small amplitude, long wavelength solitary waves in the Fermi-Pasta-Ulam model with general nearest-neighbor interaction potential. We establish global-in-time existence and stability of counter-propagating…

Analysis of PDEs · Mathematics 2009-11-13 A. Hoffman , C. E. Wayne

We study spatial pattern formation and energy localization in the dynamics of an anharmonic chain with quadratic and quartic intersite potential subject to an optical, sinusoidally oscillating field and a weak damping. The zone-boundary…

Pattern Formation and Solitons · Physics 2009-11-07 Ramaz Khomeriki , Stefano Lepri , Stefano Ruffo

We numerically study a one dimensional, nonlinear lattice model which in the linear limit is relevant to the study of bending (flexural) waves. In contrast with the classic one dimensional mass-spring system, the linear dispersion relation…

Statistical Mechanics · Physics 2022-02-16 Arnold Ngapasare , Geogios Theocharis , Olivier Richoux , Vassos Achilleos , Charalampos Skokos

The effect of discrete breathers (DBs) on macroscopic properties of the Fermi-Pasta-Ulam chain with symmetric and asymmetric potentials is investigated. The total to kinetic energy ratio (related to specific heat), stress (related to…

Based on the self-consistent $T$-matrix approximation, the quantum interference (QI) effect is studied with the diagrammatic technique in weakly-disordered two-dimensional crystals with nearly half-filled bands. In addition to the usual…

Superconductivity · Physics 2009-11-07 Y. H. Yang , D. Y. Xing , Y. G. Wang , M. Liu

The dynamics of energy relaxation in thermalized one- and two-dimensional arrays with nonlinear interactions depend in detail on the interactions and, in some cases, on dimensionality. We describe and explain these differences for arrays of…

Statistical Mechanics · Physics 2009-11-07 R. Reigada , A. Sarmiento , Katja Lindenberg

Breather stability and longevity in thermally relaxing nonlinear arrays depend sensitively on their interactions with other excitations. We review the relaxation of breathers in Fermi-Pasta-Ulam arrays, with a specific focus on the…

Statistical Mechanics · Physics 2009-11-07 Ramon Reigada , Antonio Sarmiento , Katja Lindenberg

Superconducting qubits are an attractive platform for quantum computing since they have demonstrated high-fidelity quantum gates and extensibility to modest system sizes. Nonetheless, an outstanding challenge is stabilizing their…

We prove the existence of small-amplitude periodic traveling waves in dimer Fermi-Pasta-Ulam-Tsingou (FPUT) lattices without assumptions of physical symmetry. Such lattices are infinite, one-dimensional chains of coupled particles in which…

Dynamical Systems · Mathematics 2024-12-24 Timothy E. Faver , Hermen Jan Hupkes , J. Douglas Wright

In one-dimensional translationally invariant anharmonic lattices, an extended Bloch state with two or more strongly correlated particles is usually called a quantum breather. Here we study an attractive fermionic Hubbard model with two kind…

Pattern Formation and Solitons · Physics 2007-05-23 J. C. Eilbeck , F. Palmero

The spatiotemporal propagation of a momentum excitation on the finite Fermi-Pasta-Ulam lattices is investigated. The competition between the solitary wave and phonons gives rise to interesting propagation behaviors. For a moderate…

Pattern Formation and Solitons · Physics 2013-08-14 Zongqiang Yuan , Zhigang Zheng