相关论文: Scattering by a contact potential in three and low…
We present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer…
Einstein, Podolsky, and Rosen discussed their paradox in terms of measuring the positions or momenta of two particles. These degrees of freedom can become entangled upon scattering, but how much entanglement can be created in this process?…
A consecutive formalism and analysis of exactly solvable radial reflectionless potentials with barriers, which in the spatial semiaxis of radial coordinate $r$ have one hole and one barrier, after which they fall down monotonously to zero…
We consider scattering of a three-dimensional particle on a finite family of delta potentials. For some parameter values the scattering wavenctions exhibit nodal lines in the form of closed loops, which may touch but do not entangle. The…
We study the variation of the mean cross section with the density of the samples in the quantum scattering of a particle by a disordered target. The target consists of a set of pointlike scatterers, each having an equal probability of being…
A multi-channel scattering problem is studied from a point of view of integral equations system. The system appears while natural one-particle wave function equation of the electron under action of a potential with non-intersecting ranges…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
Let $\Omega$ be a domain in $\mathbb R^N$, where $N \ge 2$ and $\partial\Omega$ is not necessarily bounded. We consider nonlinear diffusion equations of the form $\partial_t u= \Delta \phi(u)$. Let $u=u(x,t)$ be the solution of either the…
We first give the solution for the local approximation of a four parameter family of generalized one-dimensional point interactions within the framework of non-relativistic model with three neighboring $\delta$ functions. We also discuss…
We consider quantum scattering from a compactly supported potential $q$. The semiclassical limit amounts to letting the wavenumber $k \to \infty$ while rescaling the potential as $k^2 q$ (alternatively, one can scale Planck's constant…
We study the threshold scattering problem for the energy-critical nonlinear Schr\"odinger equation with a repulsive inverse-square potential $\frac{a}{|x|^2} > 0$ in dimensions $d= 4, 5, 6$. On the energy level surface determined by the…
In this paper, we study the scattering problem of the scalar wave in the traversable Lorentzian wormhole geometry. The potentials and Schr\"odinger-like equations are found in cases of the static uncharged and the charged wormholes. The…
We characterize the long range dipolar scattering in 2-dimensions. We use the analytic zero energy wavefunction including the dipolar interaction; this solution yields universal dipolar scattering properties in the threshold regime. We also…
The semi-classical limit of quantum-mechanical scattering in two dimensions (2D) is developed. We derive the Wentzel-Kramers-Brillouin and Eikonal results for 2D scattering. No backward or forward glory scattering is present in 2D. Other…
Electromagnetic wave scattering by many parallel infinite cylinders is studied asymptotically as $a\to 0$. Here $a$ is the radius of the cylinders. It is assumed that the points $\hat{x}_m$ are distributed so that…
A potential for propagation of a wave in two dimensions is constructed from a random superposition of plane waves around all propagation angles. Surprisingly, despite the lack of periodic structure, sharp Bragg diffraction of the wave is…
The coherent process of particle deflection by aligned atomic strings and planes of oriented crystals is accompanied by incoherent scattering by atomic cores. While the coherent particle deflection, described by the axial or planar averaged…
We observe that the reflection and transmission coefficients of a particle within a double, PT symmetric heterojunction with spatially varying mass, show interesting features, depending on the degree of non Hermiticity, although there is no…
The Schr\"odinger equation for a charged particle in the field of a nonrelativistic electric quadrupole in two dimensions is known to be separable in spherical coordinates. We investigate the occurrence of bound states of negative energy…
In this paper, we investigate the elastic scattering of an electron by a Yukawa potential within the framework of non-commutative (NC) geometry. We first derive the NC correction to the Yukawa potential at leading order in the NC parameter,…