Related papers: Contact interactions, self-adjoint extensions, and…
In the paper the one-dimensional one-center scattering problem with the initial potential $\alpha |x|^{-1}$ on the whole axis is treated and reduced to the search for allowable self-adjoint extensions. Using the laws of conservation as…
We show the renormalization of contact interaction for odd-wave scattering in one-dimension(1D). Based on the renormalized interaction, we exactly solve the two-body problem in a harmonic trap, and further explore the universal properties…
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 show that in two dimensions (2D) a systematic expansion of the self-energy and the effective interaction of the dilute electron gas in powers of the two-body T-matrix T_0 can be generated from the exact hierarchy of functional…
A unified S-matrix framework of quantum singular interactions is presented for the comparison of self-adjoint extensions and physical renormalization. For the long-range conformal interaction the two methods are not equivalent, with…
The one-dimensional scattering of a two body interacting system by an infinite wall is studied in a quantum-mechanical framework. This problem contains some of the dynamical features present in the collision of atomic, molecular and nuclear…
In addition to the conventional renormalized--coupling--constant picture, point interactions in dimension two and three are shown to model within a suitable energy range scattering on localized potentials, both attractive and repulsive.
We develop a theory describing neutral atoms scattering at low energies in an optical lattice. We show that for a repulsive interaction, as the microscopic scattering length increases, the effective scattering amplitude approaches a…
Physical self-adjoint extensions and their spectra of the simplest one-dimensional Hamiltonian operator in which the mass is constant except for a finite jump at one point of the real axis are correctly found. Some self-adjoint extensions…
We consider two ultracold particles confined in spherically symmetric harmonic trap and interacting via isotropic potential with absorbing boundary conditions at short range that models reactive scattering. First, we apply the contact…
The objective of the present paper is the study of a one-dimensional Hamiltonian with the interaction term given by the sum of two nonlocal attractive $\delta'$-interactions of equal strength and symmetrically located with respect to the…
We study quasi-one-dimensional scattering of one and two particles with short-range interactions on a discrete lattice model in two dimensions. One of the directions is tightly confined by an arbitrary trapping potential. We obtain the…
A complete and consistent inversion technique is proposed to derive an accurate interaction potential from an effective-range function for a given partial wave in the neutral case. First, the effective-range function is Taylor or Pad\'e…
We investigate the low-energy scattering properties of two identical particles interacting via the polarized quadrupolar interaction. It is shown that a series of $s$- and $p$-wave resonances appear for identical bosons and fermions,…
We first give the solution for the local approximation of a four parameter family of generalized one-dimensional point interactions within the framework of non-relativistic model with three neighboring $\delta$ functions. We also discuss…
Subwavelength atomic arrays are a leading platform for engineering strong light-matter interactions, presenting exciting opportunities for quantum science. However, a full understanding of their multi-excitation dynamics remains a…
The prospect of controlling entanglement in interacting quantum systems offers a myriad of technological and scientific promises, given the progress in experimental studies in systems such as ultracold trapped gases. This control is often…
Universality in physics describes how disparate systems can exhibit identical low-energy behavior. Here, we reveal a rich landscape of new universal scattering phenomena governed by the interplay between an interaction and a system's…
We consider a field theory describing interacting nonrelativistic particles of two types, which map to each other under time reversal, with point-like interaction. We identify a new type of interaction which depends on the relative velocity…
Orbital degrees of freedom play an essential role in metals, semiconductors, and strongly confined electronic systems. Experiments with ultracold atoms have used highly anisotropic confinement to explore low-dimensional physics, but…