Related papers: The Ground State Energy of a Two-Dimensional Bose …

For a dilute system of non-relativistic bosons interacting through a positive $L^1$ potential $v$ with scattering length $a$ we prove that the ground state energy density satisfies the bound $e(\rho) \geq 4\pi a \rho^2 (1+…

The ground state energy per particle of a dilute, homogeneous, two-dimensional Bose gas, in the thermodynamic limit is shown rigorously to be $E_0/N = (2\pi \hbar^2\rho /m){|\ln (\rho a^2)|^{-1}}$, to leading order, with a relative error at…

For a dilute system of non-relativistic bosons interacting through a positive potential $v$ with scattering length $a$ we prove that the ground state energy density satisfies the bound $e(\rho) \geq 4\pi a \rho^2 (1+…

We consider a Bose gas in spatial dimension $n>3$ with a repulsive, radially symmetric two-body potential $V$. In the limit of low density $\rho$, the ground state energy per particle in the thermodynamic limit is shown to be $(n-2)|\mathbb…

According to a formula that was put forward many decades ago the ground state energy per particle of an interacting, dilute Bose gas at density $\rho$ is $2\pi\hbar^2\rho a/m$ to leading order in $\rho a^3\ll 1$, where $a$ is the scattering…

The leading term of the ground state energy/particle of a dilute gas of bosons with mass $m$ in the thermodynamic limit is $2\pi \hbar^2 a \rho/m$ when the density of the gas is $\rho$, the interaction potential is non-negative and the…

We discuss recent progress in the mathematical analysis of dilute Bose gases. We review results in one to three dimensions, but the focus will be on three dimensions. In all dimensions we have a two term asymptotic expansion of the ground…

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…

For a dilute system of non-relativistic bosons interacting through a positive, radial potential $v$ with scattering length $a$ we prove that the ground state energy density satisfies the bound $e(\rho) \geq 4\pi a \rho^2 (1- C \sqrt{\rho…

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 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 prove the Lee-Huang-Yang formula for the ground state energy of the 3D Bose gas with repulsive interactions described by the exponential function, in a simultaneous limit of weak coupling and high density. In particular, we show that the…

We establish the Lee-Huang-Yang formula for the ground state energy of a dilute Bose gas for a broad class of repulsive pair-interactions in 3D as a lower bound. Our result is valid in an appropriate parameter regime of soft potentials and…

Now that the properties of low temperature Bose gases at low density, $\rho$, can be examined experimentally it is appropriate to revisit some of the formulas deduced by many authors 4-5 decades ago. One of these is that the leading term in…

We propose a new method to describe the interacting bose gas at zero temperature. We use the decomposition of the logarithm of the wave function into the irreducible $n$-point functions. We argue that in the low density limit this expansion…

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) =…

A dilute two-dimensional (2D) Bose gas at zero temperature is studied by the method developed earlier by the authors. Low density expansions are derived for the chemical potential, ground state energy, kinetic and interaction energies. The…

We consider an interacting homogeneous Bose gas at zero temperature in two spatial dimensions. The properties of the system can be calculated as an expansion in powers of g, where g is the coupling constant. We calculate the ground state…

We consider a gas of bosons interacting through a hard-sphere potential with radius $\frak{a}$ in the thermodynamic limit. We derive a simple upper bound for the ground state energy per particle at low density. Our bound captures the…

We consider a dilute gas in 3D composed of two species of bosons interacting through positive inter-species and intra-species pairwise potentials. We prove a second order expansion for the energy density in the thermodynamic limit. For the…