Related papers: Dynamics of infinite classical anharmonic crystals
A new pseudoperturbative (artificial in nature) methodical proposal [15] is used to solve for Schrodinger equation with a class of phenomenologically useful and methodically challenging anharmonice oscillator potentials V(q)=\alpha_o q^2 +…
The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…
The classical dynamics of the isotropic two-dimensional harmonic oscillator confined by an elliptic hard wall is discussed. The interplay between the harmonic potential with circular symmetry and the boundary with elliptical symmetry does…
We study the dynamics of vortices in a two-dimensional, non-equilibrium system, described by the compact Kardar-Parisi-Zhang equation, after a sudden quench across the critical region. Our exact numerical solution of the phase-ordering…
We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is…
We give an example of a one-dimensional scalar spin energy with long-range interactions not satisfying standard decay conditions and which admits a continuum approximation defined for functions u in BV((0,L),[-1,1]) taking into account the…
In this article, we study the spectral properties of the perturbation of the generalized anharmonic oscillator. We consider a piecewise H\"older continuous perturbation and investigate how the H\"older constant can affect the eigenvalues.…
We apply round-off to planar rotations, obtaining a one-parameter family of invertible maps of a two-dimensional lattice. As the angle of rotation approaches pi/2, the fourth iterate of the map produces piecewise-rectilinear motion, which…
Non-relativistic conformally invariant systems in a rotating cosmic string (conical) spacetime are analyzed at the classical and quantum levels by means of the gravitoelectromagnetic interpretation of the background. Solutions of the…
We study a Langevin equation for a particle moving in a periodic potential in the presence of viscosity $\gamma$ and subject to a further external field $\alpha$. For a suitable choice of the parameters $\alpha$ and $\gamma$ the related…
We show that electron interaction with the crystal lattice imposes stringent symmetry constrains on the orbital moment propagation. We present examples that elucidate the underlying mechanisms and reveal an additional effect of ultrafast…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
In an earlier work we showed that the gravitational interaction could be reproduced as a retarded dispersion interaction (Casimir interaction) between particles composed of hypothetical particles having harmonic oscillator interactions.…
An infinite irregular harmonic chain of particles is considered. We assume that some particles (``defects'') in the chain have masses and force constants of interaction different from the masses and the interaction constants of the other…
We consider evolution of initial disturbances in spatially extended systems with autonomous rhythmic activity, such as the heart. We consider the case when the activity is stable with respect to very smooth (changing little across the…
Slow dynamics of energy transfer between different phonon modes under the resonance conditions is considered. It may result in new effects in the inelastic and quasielastic neutron scattering spectra.
We study the energy flow of dissipative dynamics on infinite lattices, allowing the total energy to be infinite and considering formally gradient dynamics. We show that in spatial dimensions 1,2, the flow is for almost all times arbitrarily…
Considering deterministic classical lattice systems with continuous variables, we show that, if the initial conditions are sampled according to a probability distribution in which the dynamical variables are statistically independent, the…
We discuss the properties of a large number N of one-dimensional (bounded) locally periodic potential barriers in a finite interval. We show that the transmission coefficient, the scattering cross section $\sigma$, and the resonances of…
We analyze the physical mechanisms leading either to synchronization or to the formation of spatio-temporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we…