Related papers: Eigenphase preserving two-channel SUSY transformat…
The creation of artificial gauge fields in neutral ultracold atom systems has opened the possibility to study the effects of spin-orbit coupling terms in clean environments. This work considers the multi-channel scattering properties of two…
We formulate a new quasi-Hermitian delta-shell pseudopotential for higher partial wave scattering, and show that any such potential must have an energy-dependent regularization. The quasi-Hermiticity of the Hamiltonian leads to a complete…
On a supersymmetric sigma model the covariantly constant forms are related to the conserved currents that are generators of a super W-algebra extending the superconformal algebra. The existence of covariantly constant forms restricts the…
Low-energy scattering is well described by the effective-range expansion. In quantum mechanics, a tower of contact interactions can generate terms in this expansion after renormalization. Scattering parameters are also encoded in the…
We construct supersymmetric (SUSY) generalized MIC-Kepler system and show that the systems with half integral Dirac quantization condition \mu= \pm{1/2}, \pm{3/2}, \pm{5/2},..... belong to a SUSY family (hierarchy of Hamiltonian) with same…
In this work the supersymmetric technique is applied to the truncated oscillator to generate Hamiltonians ruled by second and third-order polynomial Heisenberg algebras, which are connected to the Painlev\'e IV and Painlev\'e V equations…
We revisit the total scatterings (in terms of extinction, scattering and absorption cross sections) by arbitrary clusters of nonmagnetic particles that support optically-induced magnetic responses. Our reexamination is conducted from the…
A class of shape-invariant bound-state problems which represent transitions in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels. We show that the coupled-channel…
This is the third paper in a series analyzing the asymptotic distribution of the phase shifts in the semiclassical limit. We analyze the distribution of phase shifts, or equivalently, eigenvalues of the scattering matrix, $S_h(E)$, for…
A class of shape-invariant bound-state problems which represent transition in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels as well as intensity-dependent interactions.…
By applying algebraic techniques, we construct a two-parametric family of strictly isospectral Hydrogen-like potentials as well as some of its one-parametric limits. An additional one-parametric almost isospectral family of Hydrogen-like…
We present a lattice method for determining scattering phase shifts and mixing angles for the case of an arbitrary number of coupled channels. Previous nuclear lattice effective field theory simulations were restricted to mixing of up to…
Constructing the Semi - Unitary Transformation (SUT) to obtain the supersymmetric partner Hamiltonians for a one dimensional harmonic oscillator, it has been shown that under this transformation the supersymmetric partner loses its ground…
We present an approach for obtaining eigenfunctions of periodically driven time-dependent Hamiltonians. Assuming an approximate scale separation between two spatial regions where different potentials dominate, we derive an explicit…
A conceptual bridge is provided between SUSY and the three-Hilbert-space upgrade of quantum theory a.k.a. ${\cal PT}-$symmetric or quasi-Hermitian. In particular, a natural theoretical link is found between SUSY and the presence of Kato's…
In this paper we construct $\mathcal{N}=2$ supersymmetric (SUSY) quantum mechanics over several configurations of Dirac-$\delta$ potentials from one single delta to a Dirac " comb \rq\rq. We show in detail how the building of supersymmetry…
Using a newly suggested algorithm of Gozzi, Reuter, and Thacker for calculating the excited states of one dimensional systems, we determine approximately the eigenvalues and eigenfunctions of the anharmonic oscillator, described by the…
We construct a supersymmetric quantum Hall liquid with a deformed supersymmetry. One parameter is introduced in the supersymmetric Laughlin wavefunction to realize the original Laughlin wavefunction and the Moore-Read wavefunction in two…
We determine two-particle scattering phase shifts and mixing angles for quantum theories defined with lattice regularization. The method is suitable for any nonrelativistic effective theory of point particles on the lattice. In the…
The supersymmetric (SUSY) structure of coupled-mode equations that describe scattering of optical waves in one-dimensional Bragg gratings is highlighted. This property can find applications to the synthesis of special Bragg filters and…