Related papers: Some analytic results on the FPU paradox
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…
We utilize a fractional exclusion statistics of Haldane and Wu hypothesis to study the thermodynamics of a unitary Fermi gas trapped in a harmonic oscillator potential at ultra-low finite temperature. The entropy per particle as a function…
The symmetry and resonance properties of the Fermi Pasta Ulam chain with periodic boundary conditions are exploited to construct a near-identity transformation bringing this Hamiltonian system into a particularly simple form. This…
In this paper we construct a higher order expansion of the manifold of quasi unidirectional waves in the Fermi-Pasta-Ulam (FPU) chain. We also approximate the dynamics on this manifold. As perturbation parameter we use $h^2=1/n^2$, where…
We prove the non-integrability (non-existence of additional analytic conserved quantities other than Hamiltonian) for Fermi-Pasta-Ulam (FPU) lattices by virtue of Lyapunov-Kovalevskaya- -Ziglin-Yoshida's monodromy method about the…
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 introduce and numerically study a long-range-interaction generalization of the one-dimensional Fermi-Pasta-Ulam (FPU) $\beta-$ model. The standard quartic interaction is generalized through a coupling constant that decays as $1/r^\alpha$…
We provide here an explicit example of Khinchin's idea that the validity of equilibrium statistical mechanics in high dimensional systems does not depend on the details of the dynamics. This point of view is supported by extensive numerical…
The major problem posed by the Fermi-Pasta-Ulam work was the relaxation (thermalization) of a many-body system. We review two approaches to this problem, the ergodic theory and Langevin (stochastic) equation ones, which have been applied…
In 1955, Fermi, Pasta, Ulam, and Tsingou reported recurrence over time of energy between modes in a one-dimensional array of nonlinear oscillators. Subsequently, there have been myriad numerical experiments using homogenous FPUT arrays,…
We study the slow relaxation of isolated quasi-integrable systems, focusing on the classical problem of Fermi-Pasta-Ulam-Tsingou (FPU) chain. It is well-known that the initial energy sharing between different linear-modes can be inferred by…
Strongly interacting, dilute Fermi gases exhibit a scale-invariant, universal thermodynamic behaviour. This is notoriously difficult to understand theoretically because of the absence of a small interaction parameter. Here we present a…
We study the original $\alpha$-Fermi-Pasta-Ulam (FPU) system with $N=16,32$ and $64$ masses connected by a nonlinear quadratic spring. Our approach is based on resonant wave-wave interaction theory, i.e. we assume that, in the weakly…
The interplay between chaos and thermalization in weakly non-integrable systems is a rich and complex subject. Interest in this area is further motivated by a desire to develop a unified picture of chaos for both quantum and classical…
In their seminal work, Fermi, Pasta, Ulam and Tsingou explored the connection between statistical mechanics and dynamical properties, such as chaos and ergodicity. Even today, seventy years later, the topic is not fully understood: while…
We consider a Fermi-Pasta-Ulam-Tsingou lattice with randomly varying coefficients. We discover a relatively simple condition which when placed on the nature of the randomness allows us to prove that small amplitude/long wavelength solutions…
We discuss a class of mechanical models of thermometers and their minimal requirements to determine the temperature for systems out of the common scope of thermometry. In particular we consider: 1) anharmonic chains with long time of…
It is reported that the numerical simulations of the Fermi-Pasta-Ulam problem were performed by a young lady, Mary Tsingou. After 50 years of omission, it is time for a proper recognition of her decisive contribution to the first ever…
We investigate, both analytically and numerically, dispersive fractalization and quantization of solutions to periodic linear and nonlinear Fermi-Pasta-Ulam-Tsingou systems. When subject to periodic boundary conditions and discontinuous…
All possible symmetry-determined nonlinear normal modes (also called by simple periodic orbits, one-mode solutions etc.) in both hard and soft Fermi-Pasta-Ulam-$\beta$ chains are discussed. A general method for studying their stability in…