Related papers: On discrete ground states of rotating Bose-Einstei…
Recent experimental breakthroughs in the treatment of dilute Bose gases have renewed interest in their quantum mechanical description, respectively in approximations to it. The ground state properties of dilute Bose gases confined in…
We study the degeneracy of the ground-state energy $E$ of the two-component Bose-Hubbard model and of the perturbative correction $E_1$. We show that the degeneracy properties of $E$ and $E_1$ are closely related to the connectivity…
We investigate a computational device that harnesses the effects of Bose-Einstein condensation (BEC) to accelerate the speed of finding the solution of a given optimization problem. Many computationally difficult problems, including…
The ground state of a homogeneous Bose gas of hard spheres is treated in self-consistent mean-field theory. It is shown that this approach provides an accurate description of the ground state of a Bose-Einstein condensed gas for arbitrarily…
The Bose-Einstein condensation for an ideal Bose gas and for a dilute weakly interacting Bose gas in a manifold with nonnegative Ricci curvature is investigated using the heat kernel and eigenvalue estimates of the Laplace operator. The…
We study a dilute Bose gas of atoms whose scattering length a is large compared to the range of their interaction. We calculate the energy density of the homogeneous Bose-Einstein condensate to second order in the low-density expansion,…
The ground state of a rotating Bose-Einstein condensate with attractive interaction in a quasi-one-dimensional torus is studied in terms of the ratio $\gamma$ of the mean-field interaction energy per particle to the single-particle…
We generate spin squeezed ground states in an atomic spin-1 Bose-Einstein condensate tuned nearthe quantum critical point between the polar and ferromagnetic quantum phases of the interactingspin ensemble. In contrast to typical…
We consider the time-dependent Gross-Pitaevskii equation describing the dynamics of rotating Bose-Einstein condensates and its discretization with the finite element method. We analyze a mass conserving Crank-Nicolson-type discretization…
We consider the generalized Choquard equation describing trapped electron gas in 3 dimensional case. The study of orbital stability of the energy minimizers (known as ground states) depends essentially in the local uniqueness of these…
In this paper, we prove the energy diminishing of a normalized gradient flow which provides a mathematical justification of the imaginary time method used in physical literatures to compute the ground state solution of Bose-Einstein…
We consider a Bose-Einstein condensate, which is confined in a very tight toroidal/annular trap, in the presence of a potential, which breaks the axial symmetry of the Hamiltonian. We investigate the stationary states of the condensate,…
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…
The Bose-Einstein condensates of alkali atomic gases are spinor fields with local ``spin-gauge" symmetry. This symmetry is manifested by a superfluid velocity ${\bf u}_{s}$ (or gauge field) generated by the Berry phase of the spin field. In…
Rotational Bose-Einstein condensates can exhibit quantized vortices as topological excitations. In this study, the ground and excited states of the rotational Bose-Einstein condensates are systematically studied by calculating the…
We consider Bose-Einstein condensation in flat-band models from a real-space perspective. Using a basis of compact localized states, we reformulate the minimization of the mean-field energy as a Euclidian geometry problem. Within Bogoliubov…
We mathematically and numerically study the ground states of unitary Fermi gases. Starting from the three-dimensional nonlinear Schr\"{o}dinger equation that contains a quantum pressure term and an angular momentum rotation term, we first…
In this article, we study the existence and asymptotic properties of prescribed mass standing waves for the rotating dipolar Gross-Pitaevskii equation with a harmonic potential in the unstable regime. This equation arises as an effective…
Evading the Mermin-Wagner-Hohenberg no-go theorem and revisiting with rigor the ideal Bose gas confined in a square box, we explore a discrete phase transition in two spatial dimensions. Through both analytic and numerical methods we verify…
For a fast rotating condensate in a harmonic trap, we investigate the structure of the vortex lattice using wave functions minimizing the Gross Pitaveskii energy in the Lowest Landau Level. We find that the minimizer of the energy in the…