Related papers: Analytical Results for Trapped Weakly Interacting …
We study a model of bosons in the lowest Landau level in a rotating trap where the confinement potential is a sum of a quadratic and a quartic term. The quartic term improves the stability of the system against centrifugal deconfinement and…
We establish that the ability of a localized trapping potential to bind weakly-interacting bosons is dramatically enhanced in the vicinity of the threshold of formation of the single-particle bound-state of the trap. Specifically, for…
The variational determination of the two-boson reduced density matrix is described for a one-dimensional system of $N$ (where $N$ ranges from $2$ to $10^4$) harmonically trapped bosons interacting via contact interaction. The ground-state…
We consider identical quantum bosons with weak contact interactions in a two-dimensional isotropic harmonic trap. When the interactions are turned off, the energy levels are equidistant and highly degenerate. At linear order in the coupling…
We examine the problem of two particles confined in an isotropic harmonic trap, which interact via a finite-ranged Gaussian-shaped potential in two spatial dimensions. We derive an approximative transcendental equation for the energy and…
Using Perron-Frobenius theorem, we prove that the results by Wilkin, Gunn and Smith [1] for the ground states of N Bose atoms rotating at the angular momentum L in a harmonic atomic trap with frequency omega interacting via attractive…
In these two papers, we solve the N body 1D harmonically trapped spinless Boson or spin 1/2 Fermions with repulsive delta function interaction in the limit $N\to \infty$.
I consider non-relativistic bosons interacting via pairwise potentials with infinite scattering length and supporting no two-body bound states. To lowest order in effective field theory, these conditions lead to non-interacting bosons,…
We present a non-perturbative renormalization of the bound state problem of n bosons interacting with finitely many Dirac delta interactions on two and three dimensional Riemannian manifolds using the heat kernel. We formulate the problem…
We consider systems of interacting bosons confined to one-dimensional harmonic traps. In the limit of perturbatively weak two-body interactions the system exhibits several universal states that are exact solutions for a large class of…
The Bethe roots describing the ground state energy of the integrable 1D model of interacting bosons with weakly repulsive two-body delta interactions are seen to satisfy the set of Richardson equations appearing in the strong coupling limit…
We examine the problem of a repulsive, weakly-interacting and harmonically trapped Bose-Einstein condensate under rotation. We derive a simple analytic expression for the energy incorporating the interactions when the angular momentum per…
We study a strongly interacting system of N identical bosons and one impurity in a one-dimensional trap. First, we assume that the particles have identical masses and analyze the corresponding set-up. After that, we study the influence of a…
We consider systems of a small number of interacting bosons confined to harmonic potentials in one and two dimensions. By exact numerical diagonalization of the many-body Hamiltonian we determine the low lying excitation energies and the…
We make use of a simple pair correlated wave function approach to obtain results for the ground-state densities and momentum distribution of a one-dimensional three-body bosonic system with different interactions in a harmonic trap. For…
The system of two interacting bosons in a two-dimensional harmonic trap is compared with the system consisting of two noninteracting fermions in the same potential. In particular, we discuss how the properties of the ground state of the…
We present an exact diagonalization study of the spectral properties of bosons harmonically confined in a quasi-2D plane and interacting via repulsive Gaussian potential. We consider the lowest $100$ energy levels for systems of $N=12, 16$…
The time-evolution of few number of interacting, harmonically confined one-dimensional bosons is numerically obtained for arbitrary two-body $\delta-$potential interaction strengths. It is demonstrated that the period of the motion in a…
We derive and describe a very accurate variational scheme for the ground state of the system of a few ultra-cold bosons confined in one-dimensional traps of arbitrary shapes. It is based on assumption that all inter-particle correlations…
In 1963, Lieb and Liniger solved exactly a one dimensional model of bosons interacting by a repulsive \delta-potential and calculated the ground state in the thermodynamic limit. In the present work, we extend this model to a potential of…