Related papers: Exact propagators for complex SUSY partners of rea…
It is shown that fundamental solutions $K^\sigma(x,y;t)=\langle x|e^{-i H^\sigma t}|y\rangle$ of the non-stationary Schr\"{o}dinger equation (Green functions, or propagators) for the rational extensions of the Harmonic oscillator…
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using…
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…
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…
Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. We concentrate at the transition to total synchronization. We are able to develop exact solutions for…
We construct isospectral partner potentials of a complex PT-invariant potential, viz., V(x) = V_1 sech ^2 x - i V_2 sech x tanh x using Darboux's method. Oneset of isospectral potentials are obatined which can be termed 'Satellite…
Suitable complexification of the well known solvable oscillators in one dimension is shown to give the four exactly solvable models which combine the shape- and PT-invariance. In version v2 the result is extended of the s-wave…
In direct gauge mediation, the gaugino masses are anomalously small, giving rise to a split SUSY spectrum. Here we investigate the superpartner spectrum in a minimal version of "direct gaugino mediation." We find that the sfermion masses…
In the context of a two-parameter $(\alpha, \beta)$ deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator spectrum and eigenvectors are determined…
The computation of exact barycenters for a set of discrete measures is of interest in applications where sparse solutions are desired, and to assess the quality of solutions returned by approximate algorithms and heuristics. The task is…
Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…
In this paper we present a straightforward systematic method for the exact and approximate calculation of integrals that appear in formulas for the period of anharmonic oscillators and other problems of interest in classical mechanics.
Searching for infrastructure of the quantum mechanical system, we study trajectories of the s-wave poles of the S-matrix element with respect to a real phase $\alpha$ in the complex momentum plane for a complex extension of real potentials…
The problem of approximating the discrete spectra of families of self-adjoint operators that are merely strongly continuous is addressed. It is well-known that the spectrum need not vary continuously (as a set) under strong perturbations.…
In this paper we study pseudo-multipliers associated to the harmonic oscillator (also called Hermite multipliers) belonging to the ideal of $r$-nuclear operators on Lebesgue spaces.
This paper investigates the equations of motion for a relativistic charged particle in a general magnetic field. By reformulating the dynamics in four-dimensional spacetime and separating the linear and nonlinear parts, we construct an…
This paper is devoted to the computation of discrete propagators in two-dimensional crystals and their application to a number of time dependent problems. The methods to compute such kernels are provided by a tight-binding representation of…
The main aim of the paper is to give a formula for computing the separation \L ojasiewicz exponents for two real analytic set germs via the Newton--Puiseux expansions of their defining functions. Moreover, we present an effective exponent…
Supersymmetry transformations of first and second order are used to generate Hamiltonians with known spectra departing from the harmonic oscillator with an infinite potential barrier. It is studied also the way in which the eigenfunctions…
Allowing for the inclusion of the parity operator, it is possible to construct an oscillator model whose Hamiltonian admits an EXACT square root, which is different from the conventional approach based on creation and annihilation…