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The varying-mass Schr\"odinger equation (VMSE) has been successfully applied to model electronic properties of semiconductor hetero-structures, for example, quantum dots and quantum wells. In this paper, we consider VMSE with small random…
Using a generalized transfer matrix method we exactly solve the Schr\"odinger equation in a time periodic potential, with discretized Euclidean space-time. The ground state wave function propagates in space and time with an oscillating…
Many astrophysical sources radiate via synchrotron emission from relativistic electrons. The electrons give off their kinetic energy as radiation and this radiative loss modifies the electron energy distribution. An analytical treatment of…
Transport of a particle in a spatially periodic harmonic potential under the influence of a slowly time-dependent unbiased periodic external force is studied. The equations of motion are the same as in the problem of a slowly forced…
A formulation for transport in an inhomogeneous, interacting electron gas is described. Electronic current is induced by a constraint condition imposed as a vector Lagrange multiplier. Constrained minimization of the total energy functional…
We investigate the validity of gaussian lower bounds for solutions to an electromagnetic Schr\"odinger equation with a bounded time-dependent complex electric potential and a time-independent vector magnetic potential. We prove that, if a…
The problem of Bloch electrons in two dimensions subject to magnetic and intense electric fields is investigated. Magnetic translations, electric evolution and energy translation operators are used to specify the solutions of the…
In this paper, we consider the existence and the asymptotic completeness of the wave operators for Schrodinger equations with time-dependent potentials which are short-range in space.
We theoretically consider the amplification of THz radiation in a superlattice Bloch oscillator. The main dilemma in the realization of THz Bloch oscillator is finding operational conditions which allow simultaneously to achieve gain at THz…
We propose and study a system of Schr\"odinger's problems and functional equations in probability theory. More precisely, we consider a system of variational problems of relative entropies for probability measures on a Euclidean space with…
A novel method for solving the linear radiative transport equation (RTE) in a three-dimensional homogeneous medium is proposed and illustrated with numerical examples. The method can be used with an arbitrary phase function A(s,s') with the…
Heterogeneity can be accounted for by a random potential in the wave equation. For acoustic waves in a fluid with fluctuations of both density and compressibility (as well as for electromagnetic waves in a medium with fluctuation of both…
The Schrodinger motion of a charged quantum particle in an electromagnetic potential can be simulated by the paraxial dynamics of photons propagating through a spatially inhomogeneous medium. The inhomogeneity induces geometric effects that…
The late time asymptotics of the physical solutions to the Lorentz-Dirac equation in the electromagnetic external fields of simple configurations -- the constant homogeneous field, the linearly polarized plane wave (in particular, the…
The electric and magnetic fields of a spatio-temporally varying electric current loop are calculated using the Jefimenko equations. The radiation and the nonradiation parts of the electromagnetic fields are derived in the framework of…
The Schr\"odinger equation relates the electron wavefunction and the electric potential, which are emergent physical quantities. At that emergent level, the Schr\"odinger equation is either postulated as a principle of quantum physics or…
We develop a new approach to electron transport in mesoscopic systems by using a particular single-particle basis. Although this basis generates redundant many-particle amplitudes, it greatly simplifies the treatment. By using our method…
We derive approximate iterative analytical solutions of the non-extensive Boltzmann transport equation in the relaxation time approximation. The approximate solutions almost overlap with the exact solution for a considerably wide range of…
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 consider the dynamics of noninteracting electrons on a square lattice in the presence of a magnetic flux {\alpha} and a dc electric field E oriented along the lattice diagonal. In general, the adiabatic dynamics of an electron will be…