相关论文: Symmetry of bound and antibound states in the semi…

Approximate scattering and bound state solutions of the one-dimensional effective-mass Dirac equation with the Woods-Saxon potential are obtained in terms of the hypergeometric-type functions. Transmission and reflection coefficients are…

We provide a class of lower bounds for concurrence based on symmetric measurements. We show that our lower bounds estimate the quantum entanglement better than some existing lower bounds by detailed examples. Moreover, our lower bounds can…

This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are…

Motivated by the partial differential equations of mixed type that arise in the reduction of the Einstein equations by a helical Killing vector field, we consider a boundary value problem for the helically-reduced wave equation with an…

Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size…

This article is devoted to the construction of numerical methods which remain insensitive to the smallness of the semiclassical parameter for the linear Schr{\"o}dinger equation in the semiclassical limit. We specifically analyse the…

In this paper, the interaction of an incident finite amplitude longitudinal wave with a localized region of nonlinearity is considered. This interaction produces a secondary field represented by a superposition of first-, second-, and…

We explore boundary scattering in the sine-Gordon model with a non-integrable family of Robin boundary conditions. The soliton content of the field after collision is analysed using a numerical implementation of the direct scattering…

Lattice QCD spectra can be used to constrain partial-wave scattering amplitudes that, while satisfying unitarity, do not have to respect crossing symmetry and analyticity. This becomes a particular problem when extrapolated far from real…

We study the cubic-quintic NLS in three space dimensions. It is known that scattering holds for solutions with mass-energy in a region corresponding to positive virial, the boundary of which is delineated both by ground state solitons and…

We consider the scattering of two-bosons with negative parity and spin 0 or 1. Starting from helicity partial-wave scattering amplitudes we derive transformations that eliminate all kinematical constraints. Such amplitudes are expected to…

By virtue of a weak comparison principle in small domains we prove axial symmetry in convex and symmetric smooth bounded domains as well as radial symmetry in balls for regular solutions of a class of quasi-linear elliptic systems in…

In boundary conformal field theories, global symmetries can be broken by boundary conditions, generating a homogeneous conformal manifold. We investigate these geometries, showing they have a coset structure, and give fully worked out…

We consider the N=1 supersymmetric two-dimensional non-linear sigma model with boundaries and nonzero B-field. By analysing the appropriate currents we describe the full set of boundary conditions compatible with N=1 superconformal…

For semiclassical problems we establish upper bounds on the number of resonances in boxes of size $h$ along the real axis, in terms of the dimension of the set of trapped trajectories. The proof uses second microlocalization.

We obtain an integral inequality for asymptotically linear harmonic functions on asymptotically flat 3-manifolds with noncompact boundary, which implies positivity of a convex combination of ADM masses of two conformally related metrics…

Exact positive and negative energy solutions for the eigenvalue problem of the Schr\"{o}dinger equation in one dimension with a $\delta^\prime$ interaction are found and analyzed. An infinite series of transparency resonance levels in the…

A theory of electromagnetic (EM) wave scattering by many small particles of an arbitrary shape is developed. The particles are perfectly conducting or impedance. For a small impedance particle of an arbitrary shape an explicit analytical…

By applying the supersymmetric approach we rigorously prove smoothness of the averaged density of states for a three dimensional random band matrix ensemble, in the limit of infinite volume and fixed band width. We also prove that the…

Convergence of the solutions of nonhomogeneous linear singularly perturbed systems to that of the corresponding reduced singular system on the half-line [0, $\infty $) is considered. To include the situation on a neighborhood of initial…