Related papers: Resonance asymptotics for Schrodinger operators on…
Let (M, g) be a compact smooth Riemannian manifold. We obtain new off-diagonal estimates as {\lambda} tend to infinity for the remainder in the pointwise Weyl Law for the kernel of the spectral projector of the Laplacian onto functions with…
This study is devoted to the asymptotic spectral analysis of multiscale Schr\"odinger operators with oscillating and decaying electric potentials. Different regimes, related to scaling considerations, are distinguished. By means of a normal…
Current performance bounds for randomized iterative methods are often considered tight under per-iteration analyses, yet they are notoriously loose in practice. We derive asymptotic performance bounds that narrow this theory-practice gap,…
Stationary solutions asymptoting to nonlinear plane waves of the nonlinear Schr\"odinger equation with a PT-symmetric, complex linear potential are characterized. The potential includes both a spatially varying gain-loss profile and a…
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 study the cut-off resolvent of semiclassical Schr{\"o}dinger operators on $\mathbb{R}^d$ with bounded compactly supported potentials $V$. We prove that for real energies $\lambda^2$ in a compact interval in $\mathbb{R}_+$ and for any…
This paper studies the resonances of Schr\"odinger operators with bounded, compactly supported, real-valued potentials on d-dimensional Euclidean space, where d is even. If the potential V is non-trivial and d is not 4 then the meromorphic…
We derive explicit bounds for the remainder term in the local Weyl law for locally hyperbolic manifolds, we also give the estimates of the derivative of this remainder. We use these to obtain explicit bounds for the C^k-norms of the…
We investigate a propagation of solitons for nonlinear Schr\"odinger equation under small driving force. The driving force passes through the resonance. The process of scattering on the resonance leads to changing of number of solitons.…
We prove that the imaginary parts of scattering resonances for negatively curved asymptotically hyperbolic surfaces are uniformly bounded away from zero and provide a resolvent bound in the resulting resonance-free strip. This provides an…
We characterize the local smoothness and the asymptotic growth rate of the L\'evy white noise. We do so by characterizing the weighted Besov spaces in which it is located. We extend known results in two ways. First, we obtain new bounds for…
In this paper, by a new method we establish the Weyl-type asymptotic formula for the counting function of biharmonic Stekloff eigenvalues with Neumann boundary condition in a bounded domain of an $n$-dimensional Riemannian manifold.
Suppose that $(X, g)$ is a conformally compact $(n+1)$-dimensional manifold that is hyperbolic at infinity in the sense that outside of a compact set $K \subset X$ the sectional curvatures of $g$ are identically equal to minus one. We prove…
We consider the self-adjoint Smilansky Hamiltonian $\mathsf{H}_\varepsilon$ in $L^2(\mathbb{R}^2)$ associated with the formal differential expression $-\partial_x^2 - \frac12\big(\partial_y^2 + y^2) - \sqrt{2}\varepsilon y \delta(x)$ in the…
We turn back to the well known problem of interpretation of the Schrodinger operator with the pseudopotential being the first derivative of the Dirac function. We show that the problem in its conventional formulation contains hidden…
We consider the resonances of the self-adjoint three-dimensional Schr\"odinger operator with point interactions of constant strength supported on the set $X = \{ x_n \}_{n=1}^N$. The size of $X$ is defined by $V_X = \max_{\pi\in\Pi_N}…
A waveguide coincides with a strip having two narrows of diameter $\epsilon$. Electron motion is described by the Helmholtz equation with Dirichlet boundary condition. The part of waveguide between the narrows plays the role of resonator…
The scattering of longitudinally polarized W bosons in extensions of the Standard Model with anomalous Higgs couplings to the gauge sector and higher order $O(p^4)$ operators is considered. The modified couplings should be thought as the…
In this paper, we consider the scattering theory for acoustic-type equations on non-compact manifolds with a single flat end. Our main purpose is to show an existence result of non-scattering energies. Precisely, we show a Weyl-type lower…
This paper studies the asymptotic behavior of several central objects in Dunkl theory as the dimension of the underlying space grows large. Our starting point is the observation that a recent result from the random matrix theory literature…