Related papers: Dynamics of infinite classical anharmonic crystals
We study the long-time behavior of global strong solutions to a hydrodynamic system for nonhomogeneous incompressible nematic liquid crystal flows driven by two types of external forces in a smooth bounded domain in $\mathbb{R}^2$. For…
We study "the Caged Anisotropic Harmonic Oscillator", which is a new example of a superintegrable, or accidentally degenerate Hamiltonian. The potential is that of the harmonic oscillator with rational frequency ratio (l:m:n), but…
An analytical model of high frequency oscillations of the kinetic and potential energies in a one-dimensional harmonic crystal with a substrate potential is obtained by introducing the nonlocal energies [1]. A generalization of the kinetic…
We consider a charged particle moving in the plane subject to electromagnetic potentials with non-vanishing radial limits. We analyse the classical and the quantum dynamics for large time in the case the angular part of the (limiting)…
Pair interaction potentials between atoms in a crystal are in general non-monotonic in distance, with a local minimum whose position gives the lattice constant of the crystal. A temporal analogue of this idea of crystal formation is still…
We study a system of a quantum particle interacting with a singular time-dependent uniformly rotating potential in 2 and 3 dimensions: in particular we consider an interaction with support on a point (rotating point interaction) and on a…
We consider a one-dimensional mono-atomic lattice with random perturbations of masses spread over a finite number of particles. Assuming Newtonian dynamics and linear nearest-neighbour interactions and allowing for a provision of pinning…
A two-dimensional lattice of oscillators with identical (zero) intrinsic frequencies and Kuramoto type of interactions with randomly frustrated couplings is considered. Starting the time evolution from slightly perturbed synchronized…
The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency…
We study an interacting particle system in which moving particles activate dormant particles linked by the components of critical bond percolation. Addressing a conjecture from Beckman, Dinan, Durrett, Huo, and Junge for a continuous…
We study the classical Antonov problem (of retrieving the statistical equilibrium properties of a self-gravitating gas of classical particles obeying Boltzmann statistics in space and confined in a spherical box) for a rotating system. It…
Time-decaying harmonic oscillators yield dispersive estimates with weak decay, and change the threshold power of the nonlinearity between the short and the long range. In the non-critical case for the time-decaying harmonic oscillator, this…
We consider the possibility that classical dynamical systems display motion in their lowest energy state, forming a time analogue of crystalline spatial order. Challenges facing that idea are identified and overcome. We display arbitrary…
Nematic liquid crystals in a polyhedral domain, a prototype for bistable displays, may be described by a unit-vector field subject to tangent boundary conditions. Here we consider the case of a rectangular prism. For configurations with…
An acoustic standing wave acts as a lattice of evenly spaced potential energy wells for sub-wavelength-scale objects. Trapped particles interact with each other by exchanging waves that they scatter from the standing wave. Unless the…
Conditions on the elastic stiffnesses of anisotropic crystals are derived such that circularly polarized longitudinal inhomogeneous plane waves with an isotropic slowness bivector may propagate for any given direction of the normal to the…
We examine a spatial evolution of lightwaves in a nonlinear photonic crystal with a quadratic nonlinearity when simultaneously a second harmonic and a sum-frequency generation are quasi-phase-matched. We find the conditions of a transition…
Spontaneous symmetry breaking is one of the central organizing principles in physics. Time crystals have emerged as an exotic phase of matter, spontaneously breaking the time translational symmetry, and are mainly categorized as discrete or…
We study the dynamics of nonequilibrium instabilities in anisotropically expanding systems. The most prominent example of such a system is the 'Glasma' in the context of relativistic heavy-ion collision experiments, where the expansion is a…
A periodic lattice in Euclidean space is the infinite set of all integer linear combinations of basis vectors. Any lattice can be generated by infinitely many different bases. This ambiguity was only partially resolved, but standard…