Related papers: On discrete ground states of rotating Bose-Einstei…
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 investigate $p$-orbital Bose-Einstein condensates in both the square and checkerboard lattice by numerically solving the Gross-Pitaevskii equation. The periodic potential for the latter lattice is taken exactly from the recent experiment…
We study ground states of two-component Bose-Einstein condensates (BEC) with trapping potentials in $R^2$, where the intraspecies interaction $(-a_1,-a_2)$ and the interspecies interaction $-\beta$ are both attractive, $i.e,$ $a_1$, $a_2$…
We consider a weakly-interacting, harmonically-trapped Bose-Einstein condensed gas under rotation and investigate the connection between the energies obtained from mean-field calculations and from exact diagonalizations in a subspace of…
We develop an analytic theory for the ground state patterns and their phase transitions for spin-1 Bose-Einstein condensates on a bounded domain in the presence of a uniform magnetic field. Within the Thomas-Fermi approximation, these…
A dilute Bose gas system is studied using the functional Schr\"{o}dinger picture theory. The ground state properties are obtained by solving the infinite dimensional Schr\"{o}dinger equation variationally. It is shown that a shifted…
We use exact diagonalization to study an interacting system of $N$ spinless bosons with finite-range Gaussian repulsion, confined in a quasi-two-dimensional harmonic trap with and without an introduced rotation. The diagonalization of the…
We study the nonlinear Schr\"odinger equation arising in dipolar Bose-Einstein condensate in the unstable regime. Two cases are studied: the first when the system is free, the second when gradually a trapping potential is added. In both…
We investigate the ground state properties of a gas of interacting particles confined in an external potential in three dimensions and subject to rotation around an axis of symmetry. We consider the so-called Gross-Pitaevskii (GP) limit of…
The stability of a Bose condensed gas with a negative scattering length is studied with regard to the role played by the initial state. A trapped ideal gas ground state is shown to be unstable when the Gross Pitaevskii equation still…
We consider the ground state and the low-lying excitations of dipolar Bose-Einstein condensates in a bubble trap, i.e., a shell-shaped spherically symmetric confining potential. By means of an appropriate Gaussian ansatz, we determine the…
We consider a Bose gas consisting of $N$ particles in $\mathbb{R}^3$, trapped by an external field and interacting through a two-body potential with scattering length of order $N^{-1}$. We prove that low energy states exhibit complete…
Fragmented Bose-Einstein condensates are large systems of identical bosons displaying \emph{multiple} macroscopic occupations of one-body states, in a suitable sense. The quest for an effective dynamics of the fragmented condensate at the…
We create rapidly rotating Bose-Einstein condensates in the lowest Landau level, by spinning up the condensates to rotation rates $\Omega>99%$ of the centrifugal limit for a harmonically trapped gas, while reducing the number of atoms. As a…
We consider a gas of bosonic particles confined in a box with Neumann boundary conditions. We prove Bose-Einstein condensation in the Gross-Pitaevskii regime, with an optimal bound on the condensate depletion. Our lower bound for the ground…
In the present work we revisit the problem of the quantum droplet in atomic Bose-Einstein condensates with an eye towards describing its ground state in the large density, so-called Thomas-Fermi limit. We consider the problem as being…
Recently, the simulation of moir\'e physics using cold atom platforms has gained significant attention. These platforms provide an opportunity to explore novel aspects of moir\'e physics that go beyond the limits of traditional condensed…
In this article, we derived a rigorous lower bound on the ground-state energy for a class of one-dimensional quantum systems in deformed space with minimal coordinate and momentum uncertainties, representing the absolute minimum energy that…
We study the ground state of a dilute Bose gas in a scaling limit where the Gross-Pitaevskii functional emerges. This is a repulsive non-linear Schr\"odinger functional whose quartic term is proportional to the scattering length of the…
The gradient flow with semi-implicit discretization (GFSI) is the most widely used algorithm for computing the ground state of Gross-Pitaevskii energy functional. Numerous numerical experiments have shown that the energy dissipation holds…