Related papers: Dynamics of infinite classical anharmonic crystals

Discrete time crystals are novel phases of matter that break the discrete time translational symmetry of a periodically driven system. In this work, we propose a classical system of weakly-nonlinear parametrically-driven coupled oscillators…

The regime of undamped oscillations characterizing the stellar dynamics of virialised systems is analysed within the framework of a new approach to the study of the integrals of motion. The method is relevant as far as the cosmological…

We consider the dynamics of a harmonic crystal in the half-space with zero boundary condition. It is assumed that the initial date is a random function with zero mean, finite mean energy density which also satisfies a mixing condition of…

The lattice dynamics of coesite has been studied by a combination of diffuse x-ray scattering, inelastic x-ray scattering and an ab initio lattice dynamics calculation. The combined technique gives access to the full lattice dynamics in…

We prove Lieb-Robinson bounds for the dynamics of systems with an infinite dimensional Hilbert space and generated by unbounded Hamiltonians. In particular, we consider quantum harmonic and certain anharmonic lattice systems.

In classical external gauge fields that fall off less fast than the inverse of the evolution parameter (time) of the system the implementability of a unitary perturbative scattering operator ($S$-matrix) is not guaranteed, although the…

We show that the two phases of the 4-dimensional compact U(1) lattice gauge theory are characterized by the existence or absence of an infinite current network, defining ``infinite'' on a finite lattice in a manner appropriate to the chosen…

We prove locality estimates, in the form of Lieb-Robinson bounds, for classical oscillator systems defined on a lattice. Our results hold for the harmonic system and a variety of anharmonic perturbations with long range interactions. The…

A family of discontinuous symplectic maps on the cylinder is considered. This family arises naturally in the study of nonsmooth Hamiltonian dynamics and in switched Hamiltonian systems. The transformation depends on two parameters and is a…

We consider a harmonically driven acoustic medium in the form of a (finite length) highly nonlinear granular crystal with an amplitude and frequency dependent boundary drive. Remarkably, despite the absence of a linear spectrum in the…

Complete description of the classical and quantum dynamics of a particle in an anisotropic, rotating, harmonic trap is given. The problem is studied in three dimensions and no restrictions on the geometry are imposed. In the generic case,…

Using the decay along the diagonal of the matrix representing the perturbation with respect to the Hermite basis, we prove a reducibility result in $L^2(\mathbb{R})$ for the one-dimensional quantum harmonic oscillator perturbed by time…

We study the eigenvalue problem $-u"+V(z)u=\lambda u$ in the complex plane with the boundary condition that $u(z)$ decays to zero as $z$ tends to infinity along the two rays $\arg z=-\frac{\pi}{2} \pm \frac{2\pi}{m+2}$, where…

Systems whose potential energies consists of pieces that scale as r^-2 together with pieces that scale as r^2, show no violent relaxation to Virial equilibrium but may pulsate at considerable amplitude for ever. Despite this pulsation these…

We present a microscopic theory for ultrafast control of solids with high-intensity terahertz frequency optical pulses. When resonant with selected infrared-active vibrations, these pulses transiently modify the crystal structure and lead…

The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are…

We demonstrate the emergence of a time crystal of atoms in a high-finesse optical cavity driven by a phase-modulated transverse pump field, resulting in a shaken lattice. This shaken system exhibits macroscopic oscillations in the number of…

We establish the stability of a pair of Hill's spherical vortices moving away from each other in 3D incompressible axisymmetric Euler equations without swirl. Each vortex in the pair propagates away from its odd-symmetric counterpart, while…

We consider a dynamical system, possibly infinite dimensional or non-autonomous, with fast and slow time scales which is oscillatory with high frequencies in the fast directions. We first derive and justify the limit system of the slow…

We study the propagation of energy in one-dimensional anharmonic chains subject to a periodic, localized forcing. For the purely harmonic case, forcing frequencies outside the linear spectrum produce exponentially localized responses,…