Related papers: Computing ground states of Bose-Einstein Condensat…
By examining the bound-state spectra of transverse fluctuations about one-dimensional, spatially localized dark and bright soliton wavetrains of the Gross-Pitaevskii equation, it is established that the low-temperature ground states of…
We present a generalized Gross-Pitaevskii equation that describes also the dissipative dynamics of a trapped partially Bose condensed gas. It takes the form of a complex nonlinear Schr\"odinger equation with noise. We consider an…
We compute the ground state $u$ of the Gross--Pitaevskii equation (GPE) via Wasserstein gradient descent in diffeomorphism space. We represent the density $\rho=u^2$ as the push-forward of a fixed reference measure through a parameterized…
We revisit the problem of the calculation of low-temperature properties for the dilute two-dimensional Bose gas. By using Popov's hydrodynamic approach and perturbation theory on the one-loop level we recover not only the known expansion…
We present a theory for the description of energy relaxation in a nonequilibrium condensate of bosonic particles. The approach is based on coupling to a thermal bath of other particles (e.g., phonons in a crystal, or noncondensed atoms in a…
We investigate the ground-state phases and spin-scissors dynamics of binary Bose-Einstein condensates confined in a twisted two-dimensional harmonic trap. The ground state hosts three distinct phases-phase-separated, polarized, and…
These notes present simple theoretical approaches to study Bose-Einstein condensation in trapped atomic gases and their comparison to recent experimental results : - the ideal Bose gas model - Fermi pseudopotential to model the atomic…
We investigate ground-state properties of interacting two-component Bose gases in a hard-wall trap using both the Bethe ansatz and exact numerical diagonalization method. For equal intra- and inter-atomic interaction, the system is exactly…
We investigate the spatial patterns of the ground state of two interacting Bose-Einstein condensates. We consider the general case of two different atomic species (with different mass and in different hyperfine states) trapped in a magnetic…
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 consider the nonlinear Gross-Pitaevskii equation at positive density, that is, for a bounded solution not tending to 0 at infinity. We focus on infinite ground states, which are by definition minimizers of the energy under local…
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…
Based on a generalization of Hohenberg-Kohn's theorem, we propose a ground state theory for bosonic quantum systems. Since it involves the one-particle reduced density matrix $\gamma$ as a natural variable but still recovers quantum…
We consider a Gross-Pitaevskii model of BEC with non-local interactions of range of the order of the s-wave scattering length. With this model, we study the density modulated phase in 1D and 2D, which are solutions of this modified model…
We consider the energy modeling a two component Bose-Einstein condensate in the limit of strong coupling and strong segregation. We prove the $\Gamma$-convergence to a perimeter minimization problem, with a weight given by the density of…
In this paper, we propose efficient and accurate numerical methods for computing the ground state and dynamics of the dipolar Bose-Einstein condensates utilising a newly developed dipole-dipole interaction (DDI) solver that is implemented…
We investigate vortex states in Bose-Einstein condensates under the combined action of the spin-orbit coupling (SOC), gradient magnetic field, and harmonic-oscillator trapping potential. The linear version of the system is solved exactly.…
In 1963, a Simple Approach was developed to study the ground state energy of an interacting Bose gas. It consists in the derivation of an Equation, which is not based on perturbation theory, and which gives the exact expansion of the energy…
We propose an efficient stochastic method to implement numerically the Bogolubov approach to study finite-temperature Bose-Einstein condensates. Our method is based on the Wigner representation of the density matrix describing the non…
This study proposed a new numerical scheme for vortex lattice formation in a rotating Bose-Einstein condensate (BEC) using smoothed particle hydrodynamics (SPH) with an explicit real-time integration scheme. Specifically, the…