Related papers: Exact Eigenstates for Repulsive Bosons in Two Dime…
We consider the criterion for Bose condensation for particles in a harmonic trap. For a fixed angular momentum, the lowest energy state for a cloud of bosons with attractive interactions is the ground state of the cloud with all the angular…
The eigenstates and the scattering transmission for two interacting electrons are found exactly for I quantum dots, including the hybridization with the states on the leads. The results imply limitations on the validity of the Coulomb…
Consider an N-Boson system interacting via a two-body repulsive short-range potential $V$ in a three dimensional box $\Lambda$ of side length $L$. We take the limit $N, L \to \infty$ while keeping the density $\rho = N / L^3$ fixed and…
We study various properties of bosons in two dimensions interacting only via onsite hardcore repulsion. In particular, we use the lattice spin-wave approximation to calculate the ground state energy, the density, the condensate density and…
We show that the ground state energy of the translationally invariant Nelson model, describing a particle coupled to a relativistic field of massless bosons, is an analytic function of the coupling constant and the total momentum. We derive…
Using the exact $N$-particle ground state wave function for a one-dimensional gas of hard-core bosons in a harmonic trap we develop an algorithm to compute the reduced single-particle density matrix and corresponding momentum distribution.…
For a harmonically trapped system consisting of two bosons in one spatial dimension with infinite contact repulsion (hard core bosons), we derive an expression for the one-body density matrix $\rho_B$ in terms of centre of mass and relative…
We consider $N$ trapped bosons in the mean-field limit with coupling constant $\lambda_N=1 / (N-1)$. The ground state of such systems exhibits Bose--Einstein condensation. We prove that the probability of finding $\ell$ particles outside…
Using exact diagonalization, we investigate the many-body ground state for vortex patterns in a rotating Bose-condensed gas of $N$ spinless particles, confined in a quasi-two-dimensional harmonic trap and interacting repulsively via…
We derive an integral equation describing $N$ two-dimensional bosons with zero-range interactions and solve it for the ground state energy $B_N$ by applying a stochastic diffusion Monte Carlo scheme for up to 26 particles. We confirm and go…
{}From the one-loop effective potential for a gas of non-relativistic bosons in two spatial dimensions interacting via a delta-function potential at zero-temperature and finite chemical potential, the anomaly of the energy-momentum tensor…
The ground state of bosonic atoms in a trap has been shown experimentally to display Bose-Einstein condensation (BEC). We prove this fact theoretically for bosons with two-body repulsive interaction potentials in the dilute limit, starting…
We investigate the dynamics of two bosons trapped in an infinite one-dimensional optical lattice potential within the framework of the Bose-Hubbard model and derive an exact expression for the wavefunction at finite time. As initial…
We consider the nonrelativistic four-boson system in two dimensions interacting via a short-range attractive potential. For a weakly attractive potential with one shallow two-body bound state with binding energy B_2, the binding energies…
Strongly interacting systems of dipolar bosons in three dimensions confined by harmonic traps are analyzed using the exact Path Integral Ground State Monte Carlo method. By adding a repulsive two-body potential, we find a narrow window of…
We study numerically the ground-state properties of the repulsive Hubbard model for spin-1/2 electrons on two-dimensional lattices with disordered on-site energies. The projector quantum Monte Carlo method is used to obtain very accurate…
Properties of bosonic atoms in small systems with a periodic quasi one-dimensional circular toroidal lattice potential subjected to rotation are examined by performing exact diagonalization in a truncated many body space. The expansion of…
Starting from the standard three-dimensional (3D) Gross-Pitaevskii equation (GPE) and using a variational approximation, we derive an effective one-dimensional nonpolynomial Schr\"odinger equation (1D-NPSE) governing the axial dynamics of…
We study the ground-state properties of hard-core bosons trapped by arbitrary confining potentials on one-dimensional optical lattices. A recently developed exact approach based on the Jordan-Wigner transformation is used. We analyze the…
We consider a set of electrostatic problems relevant for determining the real-space structure and the ground-state energy of a two-dimensional electron liquid subject to smooth external potentials. Three fundamental geometries are…