Related papers: Transmutation operators: construction and applicat…
We study the stationary scattering theory for the matrix Schr\"odinger equation on the half line, with the most general boundary condition at the origin, and with integrable selfadjoint matrix potentials. We prove the limiting absorption…
We show that the wave operators for Schr\"{o}dinger scattering in $\mathbb{R}^4$ have a particular form which depends on the existence of resonances. As a consequence of this form, we determine the contribution of resonances to the index of…
Exponential operator decompositions are an important tool in many fields of physics, for example, in quantum control, quantum computation, or condensed matter physics. In this work, we present a method for obtaining such decompositions,…
We consider some examples of quantum super-integrable systems and the associated nonlinear extensions of Lie algebras. The intimate relationship between super-integrability and exact solvability is illustrated. Eigenfunctions are…
The Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infinite-dimensional, it is crucial to develop finite-dimensional…
Motivated by a quaternionic formulation of quantum mechanics, we discuss quaternionic and complex linear differential equations. We touch only a few aspects of the mathematical theory, namely the resolution of the second order differential…
We prove a modified version of Turbiner's conjecture in three dimensions and we give a counter-example to the original conjecture. The Lie algebraic Schr\"odinger operators corresponding to flat metrics of a certain restricted type are…
We study various spectral theoretic aspects of non-self-adjoint operators. Specifically, we consider a class of factorable non-self-adjoint perturbations of a given unperturbed non-self-adjoint operator and provide an in-depth study of a…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
It is known that local operators in quantum field theory transform in representations of ordinary global symmetry groups. The purpose of this paper is to generalise this statement to extended operators such as line and surface defects. We…
We propose a way to study one-dimensional statistical mechanics models with complex-valued action using transfer operators. The argument consists of two steps. First, the contour of integration is deformed so that the associated transfer…
The time periodic circuit theory is exploited to introduce an appropriate translation operator that is invariant under the change of the spatial unit cell. Useful properties of the operator are derived. By casting the problem in an…
We present some old and new results on dispersive estimates for Schroedinger equations.
The Schwinger oscillator operator representation of SU(3) is analysed with particular reference to the problem of multiplicity of irreducible representations. It is shown that with the use of an $Sp(2,R)$ unitary representation commuting…
Reduction operators, i.e. the operators of nonclassical (or conditional) symmetry of a class of variable coefficient nonlinear wave equations with power nonlinearities is investigated within the framework of singular reduction operator. A…
On the basis of the explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices, we derive a new representation for the…
Koopman operator theory has been successfully applied to problems from various research areas such as fluid dynamics, molecular dynamics, climate science, engineering, and biology. Applications include detecting metastable or coherent sets,…
Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…
The scattering matrix for the full-line matrix Schr\"odinger equation is analyzed when the corresponding matrix-valued potential is selfadjoint, integrable, and has a finite first moment. The matrix-valued potential is decomposed into a…