Related papers: Improved stability for 2D attractive Bose gases
We study the ground state energy of trapped two-dimensional Bose gases with mean-field type interactions that can be attractive. We prove the stability of second kind of the many-body system and the convergence of the ground state energy…
We study the ground state properties of a one-dimensional Bose gas with N-body attractive contact interactions. By using the explicit form of the bright soliton solution of a generalized nonlinear Schroedinger equation, we compute the…
We consider a one-dimensional, trapped, focusing Bose gas where $N$ bosons interact with each other via both a two-body interaction potential of the form $a N^{\alpha-1} U(N^\alpha(x-y))$ and an attractive three-body interaction potential…
We study the ground state of a trapped Bose gas, starting from the full many-body Schr{\"o}dinger Hamiltonian, and derive the nonlinear Schr{\"o}dinger energy functional in the limit of large particle number, when the interaction potential…
We consider the dynamics of a 2D Bose gas with an interaction potential of the form $N^{2\beta-1}w(N^\beta\cdot)$ for $\beta\in (0,3/2)$. The interaction may be chosen to be negative and large, leading to the instability regime where the…
We consider a trapped Bose gas of $N$ identical bosons in two dimensional space with both an attractive, two-body, scaled interaction and a repulsive, three-body, scaled interaction respectively of the form $-aN^{2\alpha-1} U(N^\alpha…
We review our recent study on the ground state energy of dilute Bose gases with three-body interactions. The main feature of our results is the emergence of the 3D energy-critical Schr\"odinger equation to describe the ground state energy…
We examine one-dimensional Bose gas interacting with delta-function potential using the large-$N$ collective field theory. We show that in the case of attractive potential the uniform ground state is unstable to small perturbations and the…
We study a dilute gas of attractive bosons confined in a harmonic cylinder, i.e. under cylindric confinement due to a transverse harmonic potential. We introduce a many-body wave function which extends the Bethe ansatz proposed by McGuire…
We consider a trapped dilute gas of $N$ bosons in $\mathbb{R}^3$ interacting via a three-body interaction potential of the form $N\, V(N^{1/2}(x-y,x-z))$. In the limit $N\to \infty$, we prove that every approximate ground state of the…
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 exact ground state of the many-body Schr\"odinger equation for $N$ bosons on a one-dimensional ring interacting via pairwise $\delta$-function interaction is presented for up to fifty particles. The solutions are obtained by solving…
We consider the focusing 3D quantum many-body dynamic which models a dilute bose gas strongly confined in two spatial directions. We assume that the microscopic pair interaction is attractive and given by $a^{3\beta-1}V(a^{\beta}\cdot)$…
We consider a system of $N$ bosons where the particles experience a short range two-body interaction given by $N^{-1}v_N(x)=N^{3\beta-1}v(N^\beta x)$ where $v \in C^\infty_c(\mathbb{R}^3)$, without a definite sign on $v$. We extend 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…
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+…
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…
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.…
We consider a 2D quantum system of $N$ bosons in a trapping potential $|x|^s$, interacting via a pair potential of the form $N^{2\beta-1} w(N^\beta x)$. We show that for all $0 \textless{} \beta \textless{} (s+1)/(s+2)$, the leading order…
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…