Related papers: Ground State Energy of the Two-Component Charged B…

We prove upper bounds on the ground state energies of the one- and two-component charged Bose gases. The upper bound for the one-component gas agrees with the high density asymptotic formula proposed by L. Foldy in 1961. The upper bound for…

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 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.…

The model considered here is the `jellium' model in which there is a uniform, fixed background with charge density $-e\rho$ in a large volume $V$ and in which $N=\rho V$ particles of electric charge $+e$ and mass $m$ move --- the whole…

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…

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 review some rigorous estimates for the ground state energy of dilute Bose gases. We start with Dyson's upper bound, which provides the correct leading order asymptotics for hard spheres. Afterwards, we discuss a rigorous version of…

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…

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…

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…

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…

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…

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…

In 1963 a partial differential equation with a convolution non-linearity was introduced in connection with a quantum mechanical many-body problem, namely the gas of bosonic particles. This equation is mathematically interesting for several…

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 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 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(…

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…

The standard calculations of the ground-state energy of a homogeneous Bose gas rely on approximations which are physically reasonable but difficult to control. Lieb and Yngvason [Phys. Rev. Lett. 80, 2504 (1998)] have proved rigorously that…

In the present paper we study the low density Bose gas in the thermodynamic limit interacting via two-body and three-body interaction potentials. We prove that the leading order of the ground state energy is entirely characterised by both…