相关论文: Scattering of particles bounded to an infinite pla…

We study spectral and scattering properties of a spinless quantum particle confined to an infinite planar layer with hard walls containing a finite number of point perturbations. A solvable character of the model follows from the explicit…

We consider a quantum particle in a waveguide which consists of an infinite straight Dirichlet strip divided by a thin semitransparent barrier on a line parallel to the walls which is modeled by a $\delta$ potential. We show that if the…

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…

We consider a nonrelativistic quantum particle constrained to a curved layer of constant width built over a non-compact surface embedded in $R^3$. We suppose that the latter is endowed with the geodesic polar coordinates and that the layer…

We consider the nonlinear Schr{\"o}dinger equation with a short-range external potential, in a semi-classical scaling. We show that for fixed Planck constant, a com-plete scattering theory is available, showing that both the potential and…

We address the problem of transmission of electrons between two noninteracting leads through a region where they interact (quantum dot). We use a model of spinless electrons hopping on a one-dimensional lattice and with an interaction on a…

We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…

We analyze scattering in a system of two (distinguishable) particles moving on the half-line $\overline{\rz}_+$ under the influence of singular two-particle interactions. Most importantly, due to the spatial localization of the interactions…

The interaction between a Rydberg electron and a neutral atom situated inside its extended orbit is described via contact interactions for each atom-electron scattering channel. In ultracold environments, these interactions lead to…

We discuss the discrete spectrum of the Hamiltonian describing a two-dimensional quantum particle interacting with an infinite family of point interactions. We suppose that the latter are arranged into a star-shaped graph with N arms and a…

In this paper we study an interacting two-particle system on the positive half-line. We focus on spectral properties of the Hamiltonian for a large class of two-particle potentials. We characterize the essential spectrum and prove, as a…

In this paper we exploit the technique used in \cite{A}-\cite{5b} to deal with delta interactions in a rigorous way in a curved spacetime represented by a cosmic string along the $z$ axis. This mathematical machinery is applied in order to…

We consider a pair of parallel straight quantum waveguides coupled laterally through a window of a width $ \ell $ in the common boundary. We show that such a system has at least one bound state for any $ \ell>0 $. We find the corresponding…

The scattering of 1D matter wave bright solitons on attractive potentials enables one to populate bound states, a feature impossible with noninteracting wave packets. Compared to noninteracting states, the populated states are renormalized…

We study the behavior of a quantum particle confined to a hard--wall strip of a constant width in which there is a finite number $ N $ of point perturbations. Constructing the resolvent of the corresponding Hamiltonian by means of Krein's…

Scattering through a straight two-dimensional quantum waveguide Rx(0,d) with Dirichlet boundary conditions on (-\infty,0)x{y=0} \cup (0,\infty)x{y=d} and Neumann boundary condition on (-infty,0)x{y=d} \cup (0,\infty)x{y=0} is considered…

We prove an approximation result showing how operators of the type $-\Delta -\gamma \delta (x-\Gamma)$ in $L^2(\mathbb{R}^2)$, where $\Gamma$ is a graph, can be modeled in the strong resolvent sense by point-interaction Hamiltonians with an…

Wave propagation through waveguides, quantum wires or films with a modest amount of disorder is in the semi-ballistic regime when in the transversal direction(s) almost no scattering occurs, while in the long direction(s) there is so much…

Electromagnetic wave scattering by many parallel to $z-$axis, thin, impedance, circular infinite cylinders is studied asymptotically as $a\to 0$. Let $D_m$ be the crossection of the $m-$th cylinder, $a$ be its radius, and…

We consider a one-dimensional matter-wave bright soliton, corresponding to the ground bound state of N particles of mass m having a binary attractive delta potential interaction on the open line. For a full N-body quantum treatment, we…