Related papers: Scattering, homogenization and interface effects f…
A theoretical model to explain the scattering process of wave attenuation in a marginal ice zone is developed. Many field observations offer wave energy decay in the form of exponential function with distance, and this is justified through…
We study the behavior of solutions to a Schr{\"o}dinger equation with large, rapidly oscillating, mean zero, random potential with Gaussian distribution. We show that in high dimension $d>\mathfrak{m}$, where $\mathfrak{m}$ is the order of…
We consider the defocusing nonlinear Schr{\"o}dinger equation in several space dimensions, in the presence of an external potential depending on only one space vari-able. This potential is bounded from below, and may grow arbitrarily fast…
We consider the homogenization of a semilinear heat equation with vanishing viscosity and with oscillating positive potential depending on $u/\varepsilon$. According to the rate between the frequency of oscillations in the potential and the…
Recently, in Quantum Field theory, there has been an interest in scattering in highly singular potentials. Here, solutions to the stationary Schroedinger equation are presented when the potential is a multiple of an arbitrary positive power…
We consider the scattering theory for the Schrodinger equation with $-\Delta -|x|^{\alpha}$ as a reference Hamiltonian, for $0< \alpha \leq 2$, in any space dimension. We prove that when this Hamiltonian is perturbed by a potential, the…
We present a method for accurately computing transition probabilities in one-dimensional photoionization problems. Our approach involves solving the time-dependent Schr\"odinger equation and projecting its solution onto scattering states…
We consider the Dirac $\delta$-function potential problem in general case of deformed Heisenberg algebra leading to the minimal length. Exact bound and scattering solutions of the problem in quasiposition representation are presented. We…
The exact analytical solutions of the Schr\"odinger equation for the generalized symmetrical Woods-Saxon potential are examined for the scattering, bound and quasi-bound states in one dimension. The reflection and transmission coefficients…
In a previous paper by the second author, we discussed a characterization of the microlocal singularities for solutions to Schr\"odinger equations with long range type perturbations, using solutions to a Hamilton-Jacobi equation. In this…
We continue our study of scattering theory and dispersive properties for one-dimensional charge transfer models, namely linear Schr\"odinger equations with multiple moving potentials. By the discovery of a refined structure of the…
We study the homogenization of a stochastic Schr\"odinger equation with a large periodic potential in solid state physics. Denoting by $\varepsilon$ the period, the potential is scaled as $\varepsilon^{-2}$. Under a generic assumption on…
We investigate an energy-subcritical defocusing nonlinear Schr\"odinger equation in $\mathbb R^3$ subject to a lower order nonlinear trapping potential and a spatially dependent nonlinear damping: \begin{equation*} i\partial_t u + \Delta u…
In a previous paper [J. Chem. Phys. 121 4501 (2004)] a unique bipolar decomposition, Psi = Psi1 + Psi2 was presented for stationary bound states Psi of the one-dimensional Schroedinger equation, such that the components Psi1 and Psi2…
This work explores the global existence and scattering behavior of solutions to a damped, inhomogeneous nonlinear Schrodinger equation featuring a time-dependent damping term, an inverse-square potential, and an inhomogeneous nonlinearity.…
We develop a generalized theory for the scattering process produced by interface roughness on charge carriers and which is suitable for any semiconductor heterostructure. By exploiting our experimental insights into the three-dimensional…
In this paper, we study the decoherence of a wave described by the solution to a Schroedinger equation with a time-dependent random potential. The random potential is assumed to have slowly decaying correlations. The main tool to analyze…
We consider scattering waves through truncated periodic potentials with perturbations that support localized gap eigenstates. In a small complex neighborhood around an assumed positive bound state of the model operator, we prove the…
A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the…
We consider the wave equation for sound in a moving fluid with a fourth-order anomalous dispersion relation. The velocity of the fluid is a linear function of position, giving two points in the flow where the fluid velocity matches the…