Related papers: The spectral shift function for planar obstacle sc…
Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…
We consider the two-dimensional high-frequency plane wave scattering problem in the exterior of a finite collection of disjoint, compact, smooth, strictly convex obstacles with Neumann boundary conditions. Using integral equation…
We evaluate the isospin breaking corrections to the scattering amplitude \pi^- K^+ -> \pi^- K^+ at threshold in the framework of chiral perturbation theory. This channel is of particular interest for the strong 2S-2P energy level shift in…
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…
In this paper, we study the solutions to the energy-critical quadratic nonlinear Schr\"odinger system in ${\dot H}^1\times{\dot H}^1$, where the sign of its potential energy can not be determined directly. If the initial data ${\rm u}_0$ is…
Universal low-energy behaviour ${2 m c}\over{\ln |s-4m^2|}$ of the scattering function of particles of positive mass m near the threshold $s=4m^2$, and ${\pi} \over {\ln |s-4m^2|}$ for the corresponding S-wave phase-shift, is established…
We are interested in computing the spectral measure of Laplacean operators in Paley-Wiener space, the Hilbert space of all square integrable functions having Fourier transforms supported in a compact set $K$, the closure of an open bounded…
We propose a spectral quark model which can be applied to low energy hadronic physics. The approach is based on a generalization of the Lehmann representation of the quark propagator. We work at the one-quark-loop level. Electromagnetic and…
We employ the Riemann-Hilbert problem for solution of the initial-boundary value problems for nearly integrable equations on the half line which have important applications in physics. The detailed derivation of the integrable and…
In the presence of crystalline symmetries, topological phases of matter acquire a host of invariants leading to non-trivial quantized responses. Here we study a particular invariant, the discrete shift $\mathscr{S}$, for the square lattice…
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…
For a bounded open domain $\Omega\in \real^2$ with connected complement and piecewise smooth boundary, we consider the Dirichlet Laplacian $-\DO$ on $\Omega$ and the S-matrix on the complement $\Omega^c$. Using the restriction $A_E$ of…
Threshold expansions of the $\pi\pi$ and $K\overline{K}$ spin 0 and isospin 0 scattering amplitudes are performed. Scattering lengths, effective ranges and so--called volume parameters are evaluated. Good agreement with the existing…
In the Dirac-Weyl equation that describes massless neutrino propagation in the minimal Standard Model, the ($2\times 2$ equivalence of the) gamma matrices convert Weyl spinors into spacetime tensors, and vice versa. They can thus be…
We have examined cutoffs and pile-ups due to various processes in the spectra of particles produced by shock acceleration, and found that, even in the absence of energy losses, the shape of the spectrum of accelerated particles at energies…
It is shown that the Stone-von Neumann theorem is inapplicable to scattering a quantum nonrelativistic particle on a one-dimensional "short-range" potential barrier, since the unboundedness of the position operator plays here a crucial…
We employ a scalar model to exemplify the use of contour deformations when solving Lorentz-invariant integral equations for scattering amplitudes. In particular, we calculate the onshell 2 -> 2 scattering amplitude for the scalar system.…
The high energy part of the hadron spin flip amplitude is examined in the framework of the new high energy general structure (HEGS) model of the elastic hadron scattering at high energies. The different forms of the hadron spin flip…
We analyze how a short distance boundary condition for the Schrodinger equation must change as a function of the boundary radius by imposing the physical requirement of phase shift independence on the boundary condition. The resulting…
The spectral shift function of a pair of self-adjoint operators is expressed via an abstract operator valued Titchmarsh--Weyl $m$-function. This general result is applied to different self-adjoint realizations of second-order elliptic…