Related papers: The two-stage dynamics in the Fermi-Pasta-Ulam pro…
Heat conduction in low-dimensional systems exhibits strong deviations from Fourier behavior due to anharmonicity and long-lived vibrational correlations, challenging conventional computational approaches. The…
Investigating the initial conditions that lead many-body quantum systems to an out-of-equilibrium state is fundamental for understanding their thermalization dynamics. In this work we observe the relaxation for two regimes of excitation…
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…
In a growth-fragmentation system, cells grow in size slowly and split apart at random. Typically, the number of cells in the system grows exponentially and the distribution of the sizes of cells settles into an equilibrium 'asymptotic…
We analyze the interaction of a cold fast electron beam with a thermalized plasma, in the presence of many Langmuir modes. The work aims at characterizing the deviation of the system behavior from the single mode approximation, both with…
We study a slow-fast system with two slow and one fast variables. We assume that the slow manifold of the system possesses a fold and there is an equilibrium of the system in a small neighbourhood of the fold. We derive a normal form for…
The chaotic low energy region of the Fermi-Ulam simplified accelerator model is characterised by use of scaling analysis. It is shown that the average velocity and the roughness (variance of the average velocity) obey scaling functions with…
We consider a scalar Fermi-Pasta-Ulam (FPU) system on a square 2D lattice. The Kadomtsev-Petviashvili (KP-II) equation can be derived by means of multiple scale expansions to describe unidirectional long waves of small amplitude with slowly…
In this paper we study a Fermi-Ulam model where a pingpong bounces elastically against a periodically oscillating platform in a gravity field. We assume that the platform motion $f(t)$ is piecewise $C^3$ with a singularity…
The relaxation of Fourier modes of hamiltonian chains close to equilibrium is studied in the framework of a simple mode-coupling theory. Explicit estimates of the dependence of relevant time scales on the energy density (or temperature) and…
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…
A fundamental question in many-body physics is how closed quantum systems reach equilibrium. We address this question experimentally and theoretically in an ultracold large-spin Fermi gas where we find a complex interplay between internal…
We will present a survey of low energy periodic Fermi-Pasta-Ulam chains with leading idea the "breaking of symmetry". The classical periodic FPU-chain (equal masses for all particles) was analysed by Rink in 2001 with main conclusions that…
We describe the geometry of the incompressible porous medium (IPM) equation: we prove that it is a gradient dynamical system on the group of area-preserving diffeomorphisms and has a special double-bracket form. Furthermore, we show its…
A growth model which describes the deposition of particles (or the growth of a rigid crystal) on a disordered substrate is investigated. The dynamic renormalization group is applied to the stochastic growth equation using the Martin, Sigga,…
In the present paper, the pasta phase is studied at finite temperatures within a Thomas-Fermi (TF) approach. Relativistic mean field models, both with constant and density-dependent couplings, are used to describe this frustrated system. We…
Dissipation from harmonic energy eigenstates is used to characterize energy transport in binary isotopically disordered (BID) Fermi-Pasta-Ulam (FPU-beta) chains. Using a continuum analog for the corresponding harmonic portion of the…
A stochastic process, when subject to resetting to its initial condition at a constant rate, generically reaches a non-equilibrium steady state. We study analytically how the steady state is approached in time and find an unusual relaxation…
This paper investigates the stability of the power-law steady state often observed in marine ecosystems. Three dynamical systems are considered, describing the abundance of organisms as a function of body mass and time: a "jump-growth"…
In a dissipative Fermi-Pasta-Ulam-Tsingou chain particles interact with their nearest neighbors through anharmonic potentials and linear dissipative forces. We prove the existence of front solutions connecting two different uniformly…