Related papers: The Ground State Energy of a Dilute Two-dimensiona…
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…
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…
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…
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(…
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…
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…
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 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…
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…
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…
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…
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…
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…
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 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 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…
Now that the properties of the ground state 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.…
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 a dilute Bose gas in the thermodynamic limit. We prove an upper bound for the ground state energy per unit volume, capturing the expected third order term, as predicted by Wu, Hugenholtz-Pines and Sawada.