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The foundations of weak turbulence theory is explored through its application to the (alpha) Fermi-Pasta-Ulam (FPU) model, a simple weakly nonlinear dispersive system. A direct application of the standard kinetic equations would miss…
Nonlinearity shapes lattice dynamics affecting vibrational spectrum, transport and thermalization phenomena. Beside breathers and solitons one finds the third fundamental class of nonlinear modes -- $q$-breathers -- periodic orbits in…
The finest state space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation the neighborhoods of deterministic periodic orbits can be computed as distributions…
A numerical and analytical study of the relaxation to equilibrium of both the Fermi-Pasta-Ulam (FPU) alpha-model and the integrable Toda model, when the fundamental mode is initially excited, is reported. We show that the dynamics of both…
We present some analytic results aiming at explaining the lack of thermalization observed by Fermi Pasta and Ulam in their celebrated numerical experiment. In particular we focus on results which persist as the number $N$ of particles tends…
The Alpha version of the Fermi-Pasta-Ulam problem is revisited through direct numerical simulations and an application of weak turbulence theory. The energy spectrum, initialized with a large scale excitation, is traced through a series of…
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…
The inhomogeneous Fermi-Pasta-Ulam chain is studied by identifying the mass ratios that produce prominent resonances. This is a technically complicated problem as we have to solve an inverse problem for the spectrum of the corresponding…
In this paper, we consider the classic Fermi-Pasta-Ulam-Tsingou system as a model of interacting particles connected by harmonic springs with a quadratic nonlinear term (first system) and a set of second-order ordinary differential…
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…
In this letter, a multi-wave quasi-resonance framework is established to analyze energy diffusion in classical lattices, uncovering that it is fundamentally determined by the characteristics of eigenmodes. Namely, based on the presence and…
The dynamics of initial long-wavelength excitations of the Fermi-Pasta-Ulam-Tsingou chain has been the subject of intense investigations since the pioneering work of Fermi and collaborators. We have recently found a new regime where the…
We study the solutions of linear Schroedinger equations in which the potential energy is a periodic function of time and is sufficiently localized in space. We consider the potential to be close to one that is time periodic and yet…
Quantized vortices carry the angular momentum in rotating superfluids, and are key to the phenomenon of quantum turbulence. Advances in ultra-cold atom technology enable quantum turbulence to be studied in regimes with both experimental and…
Nonlinear normal modes are periodic orbits that survive in nonlinear many-body Hamiltonian systems, and their instability is crucial for relaxation dynamics. Here, we study the instability process of the $\pi/3$-mode in the…
The eigenvalue density of a quantum-mechanical system exhibits oscillations, determined by the closed orbits of the corresponding classical system; this relationship is simple and strong for waves in billiards or on manifolds, but becomes…
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…
We consider a particle governed by a one-dimensional Hamiltonian in which artificial periodic spin-orbit coupling and Zeeman lattice have incommensurate periods. Using best rational approximations to such quasiperiodic Hamiltonian, the…
The observation of the Fermi-Pasta-Ulam-Tsingou (FPUT) paradox, namely the lack of equipartition in the evolution of a normal mode in a nonlinear chain on unexpectedly long times, is arguably the most famous numerical experiment in the…
The transition from order to chaos has been a major subject of research since the work of Poincare, as it is relevant in areas ranging from the foundations of statistical physics to the stability of the solar system. Along this transition,…