Related papers: Kinetic Limit for Wave Propagation in a Random Med…
One of the central challenges in kinetic theory is the derivation of macroscopic evolution equations--describing, for example, the dynamics of an electron gas--from the underlying fundamental microscopic laws of classical or quantum…
In the setting of general initial data and whole space we perform a rigorous analysis of the quasineutral limit for a hydrodynamical model of a viscous plasma with capillarity tensor represented by the Navier Stokes Korteweg Poisson system.…
In a frame of quasi-crystal approximation the dispersion equations are obtained for the wave vector of a coherent electromagnetic wave propagating in a media which contains a random set of parallel dielectric cylinders with possible…
We study the asymptotic behavior of stochastic hyperbolic parabolic equations with slow and fast time scales. Both the strong and weak convergence in the averaging principe are established, which can be viewed as a functional law of large…
This paper develops a theory of propagation of chaos for a system of weakly interacting particles whose terminal configuration is fixed as opposed to the initial configuration as customary. Such systems are modeled by backward stochastic…
We show that the density of states of random wave equations, normalized by the square of the frequency, has a peak - sometimes narrow and sometimes broad - in the range of wave vectors between the disorder correlation length and the…
We derive the hydrodynamic limit of a kinetic equation with a stochastic, short range perturbation of the velocity operator. Under some mixing hypotheses on the stochastic perturbation, we establish a diffusion-approximation result: the…
We analyze relativistic corrections to the wave-packet dynamics of the quantum harmonic oscillator within a perturbative framework. General expressions are derived for the leading-order relativistic contributions to the wave-packet…
We develop a microscopic approach to the consistent construction of the kinetic theory of dilute weakly ionized gases of hydrogen-like atoms. The approach is based on the framework of the second quantization method in the presence of bound…
This work is devoted to the asymptotic analysis of high frequency wave propagation in random media with long-range dependence. We are interested in two asymptotic regimes, that we investigate simultaneously: the paraxial approximation,…
We study a semi-classical Schr{\"o}dinger equation which describes the dynamics of an electron in a crystal in the presence of impurities. It is well-known that under suitable assumptions on the initial data, the wave function can be…
We study the statistical fluctuations of the Casimir potential felt by an atom approaching a dielectric disordered medium. Starting from a microscopic model for the disorder, we calculate the variance of potential fluctuations in the limit…
We investigate numerically the time evolution of wave packets incident on one-dimensional semi-infinite lattices with mosaic modulated random on-site potentials, which are characterized by the integer-valued modulation period $\kappa$ and…
We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder. We study in turn: random disorder in the properties of particles; disorder in the spatial…
The formalism of generalized Wigner transformations developped in a previous paper, is applied to kinetic equations of the Lindblad type for quantum harmonic oscillator models. It is first applied to an oscillator coupled to an equilibrium…
We study the classical chaos appearing in a diatomic molecules $BeO$, $CO$ and $CN$ due to the interaction with a circularly polarized electric field, and its signature in Quantum Mechanics through the Wigner distribution function and the…
Discoveries of fundamental limits for the rates of physical processes, from the speed of light to the Lieb-Robinson bound for information propagation, often lead to breakthroughs in the our understanding of the underlying physics. Here we…
The collisionless Boltzmann equation, also called free-streaming, is a convenient approximation. It is rather simple to implement numerically, and and it is effective at reducing the irregularities of rough initial conditions. It can be…
A random matrix approach is used to analyze the vibrational properties of amorphous solids. We investigated a dynamical matrix M=AA^T with non-negative eigenvalues. The matrix A is an arbitrary real NxN sparse random matrix with n…
Dynamics is studied of an electron in a quasi-one-dimensional ballistic ring under circularly polarized electromagnetic field propagating along the normal to the ring plane. The average emission intensity from the ring is calculated. The…