Related papers: The ground state energy of a low density Bose gas:…

Consider $N$ bosons in a finite box $\Lambda= [0,L]^3\subset \mathbf R^3$ interacting via a two-body smooth repulsive short range potential. We construct a variational state which gives the following upper bound on the ground state energy…

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 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 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…

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…

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+…

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+…

We prove an upper bound for the ground state energy of a Bose gas consisting of $N$ hard spheres with radius $\mathfrak{a}/N$, moving in the three-dimensional unit torus $\Lambda$. Our estimate captures the correct asymptotics of the ground…

We investigate the properties of the ground state of a system of interacting bosons on regular lattices with coordination number $k\geq 2$. The interaction is a pure, infinite, on-site repulsion. Our concern is to give an improved upper…

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 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) =…

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…

Now that the low temperature properties of quantum-mechanical many-body systems (bosons) 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. For…

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 consider the low density Bose gas in the thermodynamic limit with a three-body interaction potential. We prove that the leading order of the ground state energy of the system is determined completely in terms of the scattering energy of…

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 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…

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 following formula for the ground state energy density of a dilute Bose gas with density $\rho$ in $2$ dimensions in the thermodynamic limit \begin{align*} e^{\rm{2D}}(\rho) = 4\pi \rho^2 Y\left(1 - Y \vert \log Y \vert + \left(…