Related papers: The Bose gas: A subtle many-body problem
The ground state of a gas of Bosons confined in an external trap potential and interacting via repulsive two-body forces has recently been shown to exhibit complete Bose-Einstein condensation in the dilute limit, yielding for the first time…
The energy and structure of a dilute hard-disks Bose gas are studied in the framework of a variational many-body approach based on a Jastrow correlated ground state wave function. The asymptotic behaviors of the radial distribution function…
We review two results in which trial states for bosonic Hamiltonians were discussed. The problem of finding a trial state for a system with a hard-core potential in the Gross-Pitaevskii regime was recently solved by proving a link with the…
A dynamical many-body theory is presented which systematically extends beyond mean-field and perturbative quantum-field theoretical procedures. It allows us to study the dynamics of strongly interacting quantum-degenerate atomic gases. The…
We consider the ground state of a trapped Bose-Einstein condensate in two dimensions. In the mean-field approximation, the ground state density profile satisfies the Gross-Pitaevskii equation. We compute the leading quantum corrections to…
We develop a quantum field theoretical framework to analytically study the three-body constrained Bose-Hubbard model beyond mean field and non-interacting spin wave approximations. It is based on an exact mapping of the constrained model to…
It has been proven theoretically for bosons with two-body repulsive interaction potentials in the dilute limit that the Gross-Pitaevskii equation provides the exact energy and density per particle as does the basic many-particle…
We analyze the scattering problem of identical bosonic particles confined on a spherical surface. At low scattering energies and for a radius much larger than the healing length, we express the contact interaction strength in terms of the…
We consider a gas of N weakly interacting bosons in the ground state. Such gases exhibit Bose-Einstein condensation. The binding energy is defined as the energy it takes to remove one particle from the gas. In this article, we prove an…
The diffusion Monte Carlo method is applied to describe a trapped atomic Bose-Einstein condensate at zero temperature, fully quantum mechanically and nonperturbatively. For low densities, $n(0)a^3 \le 2 \cdot 10^{-3}$ [n(0): peak density,…
In a recent paper we studied an equation (called the "simple equation") introduced by one of us in 1963 for an approximate correlation function associated to the ground state of an interacting Bose gas. Solving the equation yields a…
We study interacting bosons on a three-dimensional Bravais lattice with positive hopping amplitudes and on-site repulsive interactions. We prove that, in the dilute limit $\rho\to 0$, the ground state energy density satisfies $$e_0(\rho) =…
We report on ground state properties of a one-dimensional, weakly-interacting Bose gas constrained by an infinite multi-rods periodic structure at zero temperature. We solve the stationary Gross-Pitaevskii equation (GPE) to obtain the Bloch…
We consider a gas of bosons interacting through a three-body hard-core potential in the thermodynamic limit. We derive an upper bound on the ground state energy of the system at the leading order using a Jastrow factor. Our result matches…
We provide a second order energy expansion for a gas of $N$ bosonic particles with three-body interactions in the Gross-Pitaevskii regime. We especially confirm a conjecture by Nam, Ricaud and Triay in [22], where they predict the…
The ground state properties of interacting Bose gases in external potentials, as considered in recent experiments, are usually described by means of the Gross-Pitaevskii energy functional. We present here the first proof of the asymptotic…
We study the large-N limit of a system of N bosons interacting with a potential of intensity 1/N. When the ground state energy is to the first order given by Hartree's theory, we study the next order, predicted by Bogoliubov's theory. We…
We review some mathematical work on the Bose gas in the Gross-Pitaevskii regime. We start with the classical results by Lieb, Seiringer and Yngvason on the ground state energy and by Lieb and Seiringer on the existence of Bose-Einstein…
We revisit the problem of the calculation of low-temperature properties for the dilute two-dimensional Bose gas. By using Popov's hydrodynamic approach and perturbation theory on the one-loop level we recover not only the known expansion…
We consider a two-dimensional Bose gas in the dilute regime where $\rho a^2$ is small. For temperatures below the Berezinskii-Kosterlitz-Thouless critical temperature, we derive an explicit upper bound for the free energy density using…