Related papers: Radiative Transport in a Periodic Structure
I study heat and norm transport in a one-dimensional lattice of linear Schr\"odinger oscillators with conservative stochastic perturbations. Its equilibrium properties are the same of the Discrete Nonlinear Schr\"odinger equation in the…
We study numerically the dynamics of a one-electron wave packet in a two-dimensional random lattice with long-range correlated diagonal disorder in the presence of a uniform electric field. The time-dependent Schr\"{o}dinger equation is…
We considered the wave propagation between two medias. For description of physical model choose nonlinear Schredinger equation with saturation parameter. The solutions of respectively equation are found and analyzed.
We study, for times of order 1/h, solutions of Maxwell's equations in an O(h^2) modulation of an h-periodic medium. The solutions are of slowly varying amplitude type built on Bloch plane waves with wavelength of order h. We construct…
We present a physical example, where a fractional (both in space and time) Schr\"odinger equation appears only as a formal effective description of diffusive wave transport in complex inhomogeneous media. This description is a result of the…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
We study Schroedinger's equation with a potential moving along a Brownian motion path. We prove a RAGE-type theorem and Strichartz estimates for the solution on average.
In this paper, we determine the transverse instability of periodic standing wave solutions for the generalized Schr\"odinger equation with fractional power nonlinearity. The existence of periodic waves is determined by using a constrained…
We consider a model of an electron in a crystal moving under the influence of an external electric field: Schroedinger's equation in one spatial dimension with a potential which is the sum of a periodic function $V$ and a smooth function…
We consider the reflectionless transport of solitons in networks. The system is modeled in terms of the nonlinear Schr\"odinger equation on metric graphs, for which transparent boundary conditions at the branching points are imposed. This…
For an accurate treatment of the shock wave propagation in high-energy astrophysical phenomena, such as supernova shock breakouts, gamma-ray bursts and accretion disks, knowledge of radiative transfer plays a crucial role. In this paper we…
A class of periodic solutions of the nonlinear Schrodinger equation with non- Hermitian potentials are considered. The system may be implemented in planar nonlinear optical waveguides carrying an appropriate distribution of local gain and…
We investigate a propagation of solitons for nonlinear Schr\"odinger equation under small driving force. The driving force passes through the resonance. The process of scattering on the resonance leads to changing of number of solitons.…
We show how the Laplace transform can be used to give a solution of the time-dependent Schr\"odinger equation for an arbitrary initial wave packet if the solution of the stationary equation is known. The solution is obtained without summing…
We show that by integrating out the electric field and incorporating proper boundary conditions, a semiclassical Boltzmann equation can describe electron transport properties, continuously from the diffusive to ballistic regimes. General…
Existence and bifurcation results are derived for quasi periodic traveling waves of discrete nonlinear Schrodinger equations with nonlocal interactions and with polynomial type potentials. Variational tools are used. Several concrete…
Light transport in a metal with two-dimensional hole arrays is considered. Analytical expression for a transmission coefficient in periodic, isolated and disordered cases are derived, assuming the existence of waveguide modes transverse…
The basic conceptual picture and theoretical basis for development of transport equations in porous media are examined. The general form of the governing equations is derived for conservative chemical transport in heterogeneous geological…
We develop a unified approach for construction of symplectic forms for 1D integrable equations with the periodic and rapidly decaying initial data. As an example we consider the cubic nonlinear Schr\"{o}dinger equation.
The stochastic differential and integral equations describing the system of particles weakly interacting among themselves which are absorbed and scattered by particles of a medium are considered. The time-dependent transport equation with…