Related papers: The Bose gas: A subtle many-body problem
It is well known that the ground state energy of a three dimensional dilute Bose gas in the thermodynamic limit is $E=4\pi a \rho N$ when the particles interact via a non-negative, finite range, symmetric, two-body potential. Here, $N$ is…
We consider an ultracold rotating Bose gas in a harmonic trap close to the critical angular velocity so that the system can be considered to be confined to the lowest Landau level. With this assumption we prove that the Gross-Pitaevskii…
We consider the asymptotic behavior of a system of multi-component trapped bosons, when the total particle number $N$ becomes large. In the dilute regime, when the interaction potentials have the length scale of order $O(N^{-1})$, we show…
We study the ground state energy of a gas of 1D bosons with density $\rho$, interacting through a general, repulsive 2-body potential with scattering length $a$, in the dilute limit $\rho |a|\ll1$. The first terms in the expansion of the…
We consider second quantized homogeneous Bose gas in a large cubic box with periodic boundary conditions, at zero temperature. We discuss the energy-momentum spectrum of the Bose gas and its physical significance. We review various rigorous…
We investigate the dynamics of short-range interacting Bose gases with varying degrees of diluteness and interaction strength. By applying a combined mean-field and semiclassical space-time rescaling to the dynamics in both the…
We consider a gas of bosonic particles confined in a box with Neumann boundary conditions. We prove Bose-Einstein condensation in the Gross-Pitaevskii regime, with an optimal bound on the condensate depletion. Our lower bound for the ground…
A microscopic description of the zero energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the…
We study the Bose-Einstein condensates of trapped Bose gases in the Gross-Pitaevskii regime. We show that the ground state energy and ground states of the many-body quantum system are correctly described by the Gross-Pitaevskii equation in…
We determined perturbatively the low-energy universal thermodynamics of dilute one-dimensional bosons with the three-body repulsive forces. The final results are presented for the limit of vanishing potential range in terms of…
The ground-state energy per particle $E/N$ and condensate density $n_0$ of a dilute Bose gas are studied with a self-consistent perturbation expansion satisfying the Hugenholtz-Pines theorem and conservation laws simultaneously. A class of…
We establish an upper bound for the ground state energy per unit volume of a dilute Bose gas in the thermodynamic limit, capturing the correct second order term, as predicted by the Lee-Huang-Yang formula. This result has been first…
We consider N bosons in a box with volume one, interacting through a two-body potential with scattering length of the order $N^{-1+\kappa}$, for $\kappa>0$. Assuming that $\kappa\in (0;1/43)$, we show that low-energy states of the system…
This paper considers the issue of Bose-Einstein condensation in a weakly interacting Bose gas with a fixed total number of particles. We use an old current algebra formulation of non-relativistic many body systems due to Dashen and Sharp to…
We derive the asymptotic expansions of the wave function of three particles having equal mass with finite-range interactions and infinite or zero two-dimensional scattering length colliding at zero energy and zero orbital angular momentum,…
We study both Bose and Fermi gases at finite temperature and density in an approximation that sums an infinite number of many body processes that are reducible to 2-body scatterings. This is done for arbitrary negative scattering length,…
We prove an upper bound for the free energy (per unit volume) of the dilute Bose gas in the thermodynamic limit, showing that the free energy at density $\rho$ and inverse temperature $\beta$ differs from that of the non-interacting system…
We examine the possibility of Bose-Einstein condensation in one-dimensional interacting Bose gas subjected to confining potentials of the form $V_{\rm ext}(x)=V_0(|x|/a)^\gamma$, in which $\gamma < 2$, by solving the Gross-Pitaevskii…
We study the ground-state energy of N attractive bosons in the plane. The interaction is scaled for the gas to be dilute, so that the corresponding mean-field problem is a local non-linear Schr{\"o}dinger (NLS) equation. We improve the…
We review our recent study on the ground state energy of dilute Bose gases with three-body interactions. The main feature of our results is the emergence of the 3D energy-critical Schr\"odinger equation to describe the ground state energy…