Related papers: A multichannel scheme in smooth scattering theory
For scattering systems consisting of a (family of) maximal dissipative extension(s) and a selfadjoint extension of a symmetric operator with finite deficiency indices, the spectral shift function is expressed in terms of an abstract…
In the model suggested by Smilansky one studies an operator describing the interaction between a quantum graph and a system of $K$ one-dimensional oscillators attached at several different points in the graph. The present paper is the first…
We prove new criteria of stability of the absolutely continuous spectrum of one-dimensional Schr\"odinger operators under slowly decaying perturbations. As applications, we show that the absolutely continuous spectrum of the free and…
We consider the scattering problem for the nonlinear Schr\"{o}dinger equation with a potential in two space dimensions. Appropriate resolvent estimates are proved and applied to estimate the operator $A(s)$ appearing in commutator…
A spectral analysis is done on the $L$ operator of the Lax pair for the Benjamin-Ono equation. Simplicity and finiteness of the discrete spectrum are established as are needed for the Fokas and Ablowitz inverse scattering transform scheme.…
A family $A_\alpha$ of differential operators depending on a real parameter $\alpha\ge 0$ is considered. This family was suggested by Smilansky as a model of an irreversible quantum system. We find the absolutely continuous spectrum…
Inverse scattering problem for an operator, which is a sum of the operator of the third derivative and of an operator of multiplication by a real function, is solved. The main closed system of equations of inverse problem is obtained. This…
Scattering and bound states for a spinless particle in the background of a kink-like smooth step potential, added with a scalar uniform background, are considered with a general mixing of vector and scalar Lorentz structures. The problem is…
Polarization independent Mie scattering of building blocks is foundational for constructions of optical systems with robust functionalities. Conventional studies for such polarization independence are generally restricted to special states…
We show that a single-mode squeeze operator S(z) being an unitary operator with a purely continuous spectrum gives rise to a family of discrete real generalized eigenvalues. These eigenvalues are closely related to the spectral properties…
By introducing a notion of smooth connection for unbounded $KK$-cycles, we show that the Kasparov product of such cycles can be defined directly, by an algebraic formula. In order to achieve this it is necessary to develop a framework of…
A framework to calculate two-particle matrix elements for fully antisymmetrized three-cluster configurations is presented. The theory is developed for a scattering situation described in terms of the Algebraic Model. This means that the…
In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of $S$-spectrum. The proof technique consists of first establishing a spectral theorem for quaternionic bounded normal operators and…
We develop direct and inverse scattering theory for Jacobi operators which are short range perturbations of quasi-periodic finite-gap operators. We show existence of transformation operators, investigate their properties, derive the…
In our previous work, we introduced the concept of a \emph{spectral pair} for a half-line Schr\"odinger operator with a \emph{complex} bounded potential $q$, serving as a substitute for the spectral measure in a non-self-adjoint setting. In…
We consider scattering matrix for Schr\"odinger-type operators on $\mathbb{R}^d$ with perturbation $V(x)=O(\langle x\rangle^{-1})$ as $|x|\to\infty$. We show that the scattering matrix (with time-independent modifiers) is a…
The scattering of charged solitons in the complex sine-Gordon field theory is investigated. An exact factorizable S-matrix for the theory is proposed when the renormalized coupling constant takes the values $\lambda^{2}_{R}=4\pi/k$ for any…
In this paper we explore a certain class of non-selfadjoint operators acting in a complex separable Hilbert space. We consider a perturbation of a non-selfadjoint operator by an operator that is also non-selfadjoint. Our consideration is…
We consider the hamiltonian operator associated with planar sec- tions of infinitely long cylindrical solenoids and with a homogeneous magnetic field in their interior. First, in the Sobolev space $\mathcal H^2$, we characterize all…
The quaternionic spectral theorem has already been considered in the literature, see e.g. [22], [31], [32], however, except for the finite dimensional case in which the notion of spectrum is associated to an eigenvalue problem, see [21], it…