Related papers: Radiative Transport Equation for Bloch Electrons i…
We derive radiative transport equations for solutions of a Schr\"odinger equation in a periodic structure with small random inhomogeneities. We use systematically the Wigner transform and the Bloch wave expansion. The streaming part of the…
In this paper we study the asymptotic phase space energy distribution of solution of the Schr\"{o}dinger equation with a time-dependent random potential. The random potential is assumed to be with slowly decaying correlations. We show that…
We give a detailed mathematical analysis of the radiative transport limit for the average phase space density of solutions of the Schroedinger equation with time dependent random potential. Our derivation is based on the construction of an…
We use the Wigner transformation and asymptotic analysis to systematically derive the semi-classical model for the Schr\"{o}dinger equation in arbitrary spatial dimensions, with any periodic structure. Our particular emphasis lies in…
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.
This paper concerns the kinetic limit of the Dirac equation with random electromagnetic field. We give a detailed mathematical analysis of the radiative transport limit for the phase space energy density of solutions to the Dirac equation.…
The inexactness of the time-dependent Schr\"odinger equation of a charged particle in an external electromagnetic field is discussed in terms of the damping effect of the radiation. A possible improvement is to add a nonlinear term…
A set of equations is derived from the Boltzmann kinetic equation describing charge transport in semiconductors. The unknowns of these equations depend on the space-time coordinates and the electron energy. The non-parabolic and parabolic…
We propose a Schr\"odinger equation of arbitrary order for modeling charge transport in semiconductors operating in the ballistic regime. This formulation incorporates non-parabolic effects through the Kane dispersion relation, thereby…
A fourth-order Schr\"{o}dinger equation for the description of charge transport in semiconductors in the ballistic regime is proposed with the inclusion of non-parabolic effects in the dispersion relation in order to go beyond the simple…
A kinetic equation for the joint probability distribution for fixed values of the classical action, momentum and density has been derived. Further, the hydrodynamic equations of continuity and balance of momentum density have been…
A recursion technique of obtaining the asymptotical expansions for the bound-state energy eigenvalues of the radial Schr\"odinger equation with a position-dependent mass is presented. As an example of the application we calculate the energy…
We show how, beginning with the Fokker--Planck equation for electrons emitting synchrotron radiation in a storage ring, the corresponding equation for spin motion can be constructed. This is an equation of the Bloch type for the…
A Langevin equation is proposed to describe the transport of overdamped Brownian particles in a periodic rough potential and driven by an unbiased periodic force. The equation can be transformed into the Fokker-Planck equation by using the…
Schr\"odinger equation with given, {\it a priori} known current is formulated. A non-zero current density is maintained in the quantum system via a subsidiary condition imposed by vector, local Lagrange multiplier. Constrained minimization…
The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start from the standard Boltzmann equation, averaging over frequencies leads to appearance of fractional derivative. This fact is in accordance…
The Schr\"odinger equation is solved for the wave function of an electron moving in a superposition of external constant and uniform electric and magnetic fields at an arbitrary angle between the field directions. The changing of the…
We derive quantum Boltzmann equations from Schwinger-Dyson equations in gradient expansion for a weakly coupled scalar field theory with a spatially varying mass. We find that at higher order in gradients a full description of the system…
Schrodinger equation with two-component wave function which describes a relativistic spin 1/2 particle in a weak electromagnetic field is obtained. In the same approximation Schrodinger equation with traditional norm condition and…
Starting with the many-body Schr\"odinger equation we derive new rate equations for resonant transport in quantum dots linked by ballistic channels with high density of states. The charging and the Pauli exclusion principle effects were…