Related papers: Computable Error Estimates for Ground State Soluti…
We investigate the behavior of solutions of the complex Gross-Pitaevskii equation, a model that describes the dynamics of pumped decaying Bose-Einstein condensates. The stationary radially symmetric solutions of the equation are studied and…
We introduce a hybrid high-order method for approximating the ground state of the nonlinear Gross--Pitaevskii eigenvalue problem. Optimal convergence rates are proved for the ground state approximation, as well as for the associated…
This article deals with the stationary Gross-Pitaevskii non-linear eigenvalue problem in the presence of a rotating magnetic field that is used to model macroscopic quantum effects such as Bose-Einstein condensates (BECs). In this regime,…
We calculate the ground states of a dipolar Bose gas confined in an infinite tube potential. We use the extended Gross-Pitaevskii equation theory and present a novel numerical method to efficiently obtain solutions. A key feature of this…
The modified Gross-Pitaevskii equation was derived and solved to obtain the 1D solution in the zero-energy limit. This stationary solution could account for the dominated contributions due to the kinetic effect as well as the chemical…
Within the self-consistent Hartree-Fock approximation, an explicit expression for the ground state energy of inhomogeneous Bose gas is derived as a functional of the inhomogeneous density of the Bose-Einstein condensate. The results…
We solve the time-independent Gross-Pitaevskii equation modeling the Bose-Einstein condensate trapped in an anistropic harmonic potential using a pseudospectral method. Numerically obtained values for an energy and a chemical potential for…
We verify Bogoliubov's approximation for translation invariant Bose gases in the mean field regime, i.e. we prove that the ground state energy $E_N$ is given by $E_N=Ne_\mathrm{H}+\inf \sigma\left(\mathbb{H}\right)+o_{N\rightarrow…
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 analyze the corrections caused by finite size effects upon the ground state properties of a homogeneous one-dimensional Bose-Einstein condensate. We assume from the very beginning that the Bogoliubov's formalism is valid and consequently…
We consider a dilute and ultracold bosonic gas of weakly-interacting atoms. Within the framework of quantum field theory we derive a zero-temperature modified Gross-Pitaevskii equation with beyond-mean-field corrections due to quantum…
Momentum distributions and temporal power spectra of nonzero temperature Bose-Einstein condensates are calculated using a Gross-Pitaevskii model. The distributions are obtained for micro-canonical ensembles (conservative Gross-Pitaevskii…
The low-energy-level macroscopic wave functions of the Bose-Einstein condensate(BEC) trapped in a symmetric double-well and a periodic potential are obtained by solving the Gross-Pitaevskii equation numerically. The ground state tunnel…
Describing partially-condensed Bose gases poses a long-standing theoretical challenge. We present exact stochastic Ehrenfest relations for the stochastic projected Gross-Pitaevskii equation, including both number and energy damping…
We consider a gas of $N$ bosons in a box with volume one interacting through a two-body potential with scattering length of order $N^{-1}$ (Gross-Pitaevskii limit). Assuming the (unscaled) potential to be sufficiently small, we show that…
We identify all possible classes of solutions for two-component Bose-Einstein condensates (BECs) within the Thomas-Fermi (TF) approximation, and check these results against numerical simulations of the coupled Gross-Pitaevskii equations…
In this article, we propose an efficient and spectrally accurate numerical method to compute the ground states of three-dimensional (3D) rotating dipolar Bose-Einstein condensates (BEC) under strongly anisotropic trapping potentials.The…
We consider a gas of weakly interacting bosons in three dimensions subject to an external potential in the mean field regime. Assuming that the initial state of our system is a product state, we show that in the trace topology of one-body…
We develop a tensor network framework based on the quantic tensor train (QTT) format to efficiently solve the Gross-Pitaevskii equation (GPE), which governs Bose-Einstein condensates under mean-field theory. By adapting time-dependent…
We present variational calculations using a Gaussian trial function to calculate the ground state of the Gross-Pitaevskii equation and to describe the dynamics of the quasi-two-dimensional solitons in dipolar Bose-Einstein condensates.…