Related papers: A model study on a pair of trapped particles inter…
In this paper, we develop a large-$N$ field theory for a system of $N$ classical particles in one dimension at thermal equilibrium. The particles are confined by an arbitrary external potential, $V_\text{ex} (x)$, and repel each other via a…
For one-dimensional systems with delta-contact interactions, the convergence of the exact-diagonalization method is tested with a basis of harmonic oscillator eigenfunctions with frequency $\Omega$ optimized through the minimization of the…
Condensates of active particles such as cells form almost-crystalline lattices which play a central role in many biological systems. Typically, their properties have been determined merely by analogy to the rather trivial one-dimensional…
We study a two-dimensional system of two Coulombically interacting electrons in an external harmonic confining potential. More precisely, we present calculations for the singlet ground-state of the system. We explain the nature of the…
We study normal state properties of an interacting Fermi gas in an isotropic harmonic trap of arbitrary dimensions. We exactly calculate the first-order perturbation terms in the ground state energy and chemical potential, and obtain simple…
The behavior of ultracold atomic gases depends crucially on the two-body scattering properties of these systems. We develop a multichannel scattering theory for atom-atom collisions in quasi-one-dimensional (quasi-1D) geometries such as…
We use a BCS-type variational wavefunction to study attractively-interacting quasi one-dimensional (1D) fermionic atomic gases, motivated by cold-atom experiments that access the 1D regime using an anisotropic harmonic trapping potential…
We propose a discrete-space representation of a one-dimensional zero-range odd-parity pseudopotential. The proposed representation is validated by applying it to the analytically solvable case of two fermions in a harmonic trap and…
A model operator $H$ associated to a system of three-particles on the three dimensional lattice $\Z^3$ and interacting via pair non-local potentials is studied. The following results are proven: (i) the operator $H$ has infinitely many…
The sensitivity of atom interferometers depends on their ability to realize long pulse separation times and prevent loss of contrast by limiting the expansion of the atomic ensemble within the interferometer beam through matter-wave…
We consider the quantum evolution of a pair of interacting atoms in a three dimensional isotropic trap where the interaction strength is quenched from one value to another. Using exact solutions of the static problem we are able to evaluate…
We consider the resonance interaction energy between two identical entangled atoms, where one is in the excited state and the other in the ground state. They interact with the quantum electromagnetic field in the vacuum state and are placed…
We consider a large class of interacting particle systems in 1D described by an energy whose interaction potential is singular and non-local. This class covers Riesz gases (in particular, log gases) and applications to plasticity and…
We consider the feasibility of observing a trap-induced resonance [Stock et al., Phys. Rev. Lett. 91, 183201 (2003)] for the case of two 133Cs atoms, trapped in separated wells of a polarization-gradient optical lattice, and interacting…
We calculate the renormalized effective 2-, 3-, and 4-body interactions for N neutral ultracold bosons in the ground state of an isotropic harmonic trap, assuming 2-body interactions modeled with the combination of a zero-range and…
We develop a simple model of shape resonances in electron-molecule collisions that is based on the modified effective-range expansion and analytical solutions of the Schrodinger equation for the long-range part of the interaction potential.…
We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians…
A system of N two-dimensional weakly interacting bosons in a harmonic trap is considered. When the two-particle potential is a delta function Smith and Wilkin have analytically proved that the elementary symmetric polynomials of particle…
The probability amplitude for $N$ particles in a quantum gas with negligible range of interparticle interaction potentials to come to a small region of size $r$ scales like $r^\gamma$. It is shown that $\gamma$ is quantitatively related to…
We present an exact solution of a 1D model: a particle of incident energy $E$ colliding with a target which is a 1D harmonic ``solid slab'' with $N$ atoms in its ground state; the Hilbert space of the target is restricted to the ($N+1$)…