Related papers: Variations on the Fermi-Pasta-Ulam chain, a survey
We demonstrate that the modulation instability of the zone boundary mode in a finite (periodic) Fermi-Pasta-Ulam chain is the necessary but not sufficient condition for the efficient energy transfer by localized excitations. This transfer…
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…
We consider classical hard-core particles moving on two parallel chains in the same direction. An interaction between the channels is included via the hopping rates. For a ring, the stationary state has a product form. For the case of…
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…
We study the statistics and short-times dynamics of the classical and the quantum Fermi-Pasta-Ulam chain in thermal equilibrium. We analyze the distributions of single-particle configurations by integrating out the rest of the system. At…
We prove Nishida's 1971 conjecture stating that almost all low-energetic motions of the anharmonic Fermi-Pasta-Ulam lattice with fixed endpoints are quasi-periodic. The proof is based on the formal computations of Nishida, the KAM theorem,…
We study bifurcations of periodic travelling waves in granular dimer chains from the anti-continuum limit, when the mass ratio between the light and heavy beads is zero. We show that every limiting periodic wave is uniquely continued with…
We study a bipartite collective spin-$1$ model with exchange interaction between the spins. The bipartite nature of the model manifests itself by the spins being divided into two equal-sized subsystems; within each subsystem the spin-spin…
We study the dynamics of the "externally" forced and damped Fermi-Pasta-Ulam (FPU) 1D lattice. The forcing has the spatial symmetry of the Fourier mode with wavenumber p and oscillates sinusoidally in time with the frequency omega. When…
We consider a diatomic infinite Fermi-Pasta-Ulam (FPU) system with light and heavy particles. For a small mass ratio, we prove error estimates for the approximation of the dynamics of this system by the dynamics of the monoatomic FPU…
We propose an extension of the Standard Model (SM) based on the $SU(3)_C\otimes SU(3)_L\otimes U(1)_X$ (3-3-1) gauge symmetry and scale invariance. Maintaining the main features of the so-called 3-3-1 models, such as the cancellation of…
We present a family-non-universal extension of the Standard Model where the the first two families feature both quark-lepton and electroweak-flavour unification, via the $SU(4) \times Sp(4)_L \times Sp(4)_R$ gauge group, whereas…
A phenomenological approach for the universal mass matrix model with a broken flavor 2 <-> 3 symmetry is explored by introducing the 2 <-> 3 antisymmetric parts of mass matrices for quarks and charged leptons . We present explicit texture…
We propose a new mechanism in which the generation of the supersymmetric $\mu $-term as well charged lepton masses is closely tied to R-parity violation involving heavy vector-like families . A realistic example based on $SU(3)_c\times…
Simulations of pure-gauge SU(2) lattice gauge theory are performed in the minimal Coulomb gauge. This leaves a residual or remnant gauge symmetry still active which is global in three directions but still local in one. Using averaged…
We consider the neutrino physics of models with a sequentially broken U(2) flavor symmetry. Such theories yield the observed pattern of quark and lepton masses, while maintaining sufficient degeneracies between superparticles of the first…
We show that in the semiclassical limit, classically chaotic systems have universal spectral statistics. Concentrating on short-time statistics, we identify the pairs of classical periodic orbits determining the small-$\tau$ behavior of the…
Fermion mass models usually contain a horizontal symmetry and therefore fail to predict the exponential mass spectrum of the Standard Model in a natural way. In dynamical symmetry breaking there are different concepts to introduce a fermion…
A data-driven approach based on unsupervised machine learning is proposed to infer the intrinsic dimension $m^{\ast}$ of the high-dimensional trajectories of the Fermi-Pasta-Ulam-Tsingou (FPUT) model. Principal component analysis (PCA) is…
In the present work we study the Fermi--Pasta--Ulam (FPU) $\beta $--model involving long--range interactions (LRI) in both the quadratic and quartic potentials, by introducing two independent exponents $\alpha_1$ and $\alpha_2$…