Related papers: Ablowitz-Ladik system with discrete potential. I. …
Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of…
Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave…
We prove semiclassical resolvent estimates for the Schr{\"o}dinger operator in R d , d $\ge$ 3, with real-valued radial potentials V $\in$ L $\infty$ (R d). In particular, we show that if V (x) = O x --$\delta$ with $\delta$ > 2, then the…
We furnish a simple way of constructing an unbounded closed linear operator in a complex Banach space, whose spectrum is an arbitrary nonempty closed, in particular compact, subset of the complex plane.
We prove that canonical Dirac expression with linear potential generates operators on axis and half axis, for which we can find the eigenvalues and eigenfunctions in explicit form. We construct the perturbations of these operators with in…
In this paper, we propose a soliton gas solution for the focusing Ablowitz-Ladik system. This solution is defined as the large N limit of the N-soliton solution, and arises from a continuous spectrum of poles that accumulate within two…
We construct a variety of new exactly-solvable quantum systems, the potentials of which are given in terms of Lambert-W functions. In particular, we generate Schr\"odinger models with energy-dependent potentials, conventional Schr\"odinger…
An approach is proposed for bounding the number of zeros that solutions of linear differential systems with polynomial coefficients may have. A bound is obtained in a special case which improves upon currently existing.
Continuum limits of Laplace operators on general lattices are considered, and it is shown that these operators converge to elliptic operators on the Euclidean space in the sense of the generalized norm resolvent convergence. We then study…
We consider, for $h, E > 0$, resolvent estimates for the semiclassical Schr\"odinger operator $-h^2 \Delta + V - E$. Near infinity, the potential takes the form $V = V_L+ V_S$, where $V_L$ is a long range potential which is Lipschitz with…
We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted L^p-spaces over B, 1 < p < \infty. Under suitable ellipticity…
In the paper under review, we construct complex powers of multivalued linear operators with polynomially bounded $C$-resolvent existing on an appropriate region of the complex plane containing the interval $(-\infty,0].$ In our approach,…
In this note, uniform bounds of the Birman-Schwinger operators in the discrete setting are studied. For uniformly decaying potentials, we obtain the same bound as in the continuous setting. However, for non-uniformly decaying potential, our…
We construct a singular differential operator attached to a class of singular metrics on the line bundles over the complex projective space, $\mathbb{P}^1$. This operator extends the classical notion of the generalized Laplacian. We prove…
Let $H$ be a Schr\"odinger type operator with long-range perturbation. We study the wave front set of the distribution kernel of $(H-\lambda\mp i0)^{-1}$, where $\lambda$ is in the absolutely continous spectrumof $H$.The result is a…
The norm resolvent convergence of a family of one-dimensional Schroedinger operators with singular magnetic and electric potentials of small support is studied.
We consider a phase-field model where the internal energy depends on the order parameter in a nonlocal way. Therefore, the resulting system consists of the energy balance equation coupled with a nonlinear and nonlocal ODE for the order…
The relativistic bound-state energy spectrum and the wavefunctions for the Coulomb potential are studied for de Sitter and anti-de Sitter spaces in the context of the extended uncertainty principle. Klein-Gordon and Dirac equations are…
We investigate the properties of self-adjointness of a two-dimensional Dirac operator on an infinite sector with infinite mass boundary conditions and in presence of a Coulomb-type potential with the singularity placed on the vertex. In the…
We present a detailed study of the scattering system given by the Neumann Laplacian on the discrete half-space perturbed by a periodic potential at the boundary. We derive asymptotic resolvent expansions at thresholds and eigenvalues, we…