Related papers: 5/6-Superdiffusion of energy for coupled charged h…
We consider an infinite harmonic chain of charged particles submitted to the action of a magnetic field of intensity $B$ and subject to the action of a stochastic noise conserving the energy. In arXiv:0809.0177 and arXiv:1402.2988 it has…
We consider a one dimensional infinite chain of har- monic oscillators whose dynamics is perturbed by a stochastic term conserving energy and momentum. We prove that in the unpinned case the macroscopic evolution of the energy converges to…
We study the energy diffusion in a chain of anharmonic oscillators where the Hamiltonian dynamics is perturbed by a local energy conserving noise. We prove that under diffusive rescaling of space-time, energy fluctuations diffuse and evolve…
We consider a linear phonon Boltzmann equation with a reflecting/transmitting/absorbing interface. This equation appears as the Boltzmann-Grad limit for the energy density function of a harmonic chain of oscillators with inter-particle…
Consider the motion of a charged, point particle moving in the complement of a Poisson distribution of hard sphere scatterers in two dimensions under the effect of a fixed magnetic field. Building on, and extending a coupling method…
We consider an infinite chain of coupled harmonic oscillators with a Langevin thermostat attached at the origin and energy, momentum and volume conserving noise that models the collisions between atoms. The noise is rarefied in the limit,…
We consider a harmonic chain perturbed by an energy conserving noise and show that after a space-time rescaling the energy-energy correlation function is given by the solution of a skew-fractional heat equation with exponent 3/4.
We consider one-dimensional infinite chains of harmonic oscillators with stochastic perturbations and long-range interactions which have polynomial decay rate $|x|^{-\theta}, x \to \infty, \theta > 1$, where $x \in \mathbb{Z}$ is the…
In this paper we study the phenomenon of nonlinear supratransmission in a semi-infinite discrete chain of coupled oscillators described by modified sine-Gordon equations with constant external and internal damping, and subject to harmonic…
We consider a one dimensional infinite acoustic chain of harmonic oscillators whose dynamics is perturbed by a random exchange of velocities, such that the energy and momentum of the chain are conserved. Consequently, the evolution of the…
The linear Boltzmann equation for elastic and/or inelastic scattering is applied to derive the distribution function of a spatially homogeneous system of charged particles spreading in a host medium of two-level atoms and subjected to…
We consider the long time evolution of a quantum particle weakly interacting with a phonon field. We show that in the weak coupling limit the Wigner distribution of the electron density matrix converges to the solution of the linear…
We consider one-dimensional infinite chains of harmonic oscillators with random exchanges of momenta and long-range interaction potentials which have polynomial decay rate $|x|^{-\theta}, x \to \infty, \theta > 1$ where $x \in \mathbb{Z}$…
We consider a non acoustic chain of harmonic oscillators with the dynamics perturbed by a random local exchange of momentum, such that energy and momentum are conserved. The macroscopic limits of the energy density, momentum and the…
We study the fluctuations of the phonon modes in a one-dimensional chain of anharmonic oscillators where the deterministic Hamiltonian dynamics is perturbed by random exchanges of momentum between nearest neighbor particles. There are three…
The diffusion limit of the linear Boltzmann equation with a strong magnetic field is performed. The giration period of particles around the magnetic field is assumed to be much smaller than the collision relaxation time which is supposed to…
We study a system of charged, noninteracting classical particles moving in a Poisson distribution of hard-disk scatterers in two dimensions, under the effect of a magnetic field perpendicular to the plane. We prove that, in the low-density…
The theory of Raman scattering by the electron--phonon coupled system in metals and heavily doped semiconductors is developed taking into account the Coulomb screening and the electron--phonon deformation interaction. The Boltzmann equation…
Spin transport properties at finite electric and magnetic fields are studied by using the generalized semiclassical Boltzmann equation. It is found that the spin diffusion equation for non-equilibrium spin density and spin currents involves…
In earlier work we showed that the particle displacement for the multidimensional periodic Lorentz gas, in the limit of low scatterer density (Boltzmann-Grad limit), satisfies a central limit theorem with superdiffusive scaling. The present…