Related papers: An efficient Fourier spectral algorithm for the Bo…
We introduce a fast Fourier spectral method for the multi-species Boltzmann collision operator. The method retains the riveting properties of the single-species fast spectral method (Gamba et al. SIAM J. Sci. Comput., 39 pp. B658--B674…
We propose and demonstrate an echo method to reduce the inhomogeneous linewidth of Bogoliubov excitations, in a harmonically-trapped Bose-Einstein condensate. Our proposal includes the transfer of excitations with momentum +q to -q using a…
An efficient multigrid method is proposed to compute the ground state solution of Bose-Einstein condensations by the finite element method based on the combination of the multigrid method for nonlinear eigenvalue problem and an efficient…
The work reported in this article presents a high-order, stable, and efficient Gegenbauer pseudospectral method to solve numerically a wide variety of mathematical models. The proposed numerical scheme exploits the stability and the…
The condition for the appearance of dynamical instability of the Bose-condensed system, characterized by the emergence of complex eigenvalues in the Bogoliubov-de Gennes equations, is studied analytically. We perturbatively expand both the…
The ground and excited states of a weakly interacting and dilute Bose-Einstein condensed gas, confined in a completely anisotropic harmonic oscillator potential, are determined at zero temperature within the Bogoliubov approximation. The…
We develop a unified Petrov-Galerkin spectral method for a class of fractional partial differential equations with two-sided derivatives and constant coefficients of the form $ _{0}{\mathcal{D}}_{t}^{2\tau}u^{} + \sum_{i=1}^{d}$ $[c_{l_i}$…
We present a method for computing first order asymptotics of semiclassical spectra for 1-D Bogoliubov-de Gennes (BdG) Hamiltonian from Supraconductivity, which models the electron/hole scattering through two SNS junctions. This involves: 1)…
In this paper, we propose a robust and efficient numerical method to compute the dynamics of the rotating two-component dipolar Bose-Einstein condensates (BEC). Using the rotating Lagrangian coordinates transform \cite{BMTZ2013}, we…
We measure the response of an elongated Bose-Einstein condensate to a two-photon Bragg pulse. If the duration of the pulse is long, the total momentum transferred to the condensate exhibits a nontrivial behavior which reflects the structure…
This work addresses a central challenge in the numerical analysis of the cutoff spatially homogeneous Boltzmann equation: the development of rigorously justified, accurate numerical schemes. We present (i) a novel Fourier spectral method…
We present a method of finding approximate analytical solutions for the spectra and eigenvectors of collective modes in a two-dimensional system of interacting bosons subjected to a linear external potential or the potential of a special…
We investigate spectral stability of vortex solutions of the Gross-Pitaevskii equation, a mean-field approximation for Bose-Einstein condensates (BEC) in an effectively two-dimensional axisymmetric harmonic trap. We study eigenvalues of the…
An exact-diagonalization technique on finite-size clusters is used to study the ground state and excitation spectra of the two-dimensional effective fermion model, a fictious model of hole quasiparticles derived from numerical studies of…
This paper investigates the dynamics of spin-2 Bose-Einstein condensates (BECs) with rotation and spin-orbit coupling (SOC). In order to better simulate the dynamics, we present an efficient high-order compact splitting Fourier spectral…
The complete low-energy collective-excitation spectrum of vortex lattices is discussed for rotating Bose-Einstein condensates (BEC) by solving the Bogoliubov-de Gennes (BdG) equation, yielding, e.g., the Tkachenko mode recently observed at…
The Bogoliubov approximation is used to study the excited states of a dilute gas of $N$ atomic bosons trapped in an isotropic harmonic potential characterized by a frequency $\omega_0$ and an oscillator length $d_0 =…
We study density and spin excitations of one-dimensional self-bound Bose-Bose droplets within Bogoliubov theory, and show that spin excitations come alive, especially as the interspecies coupling is made less attractive. We argue that spin…
We present a detailed study of the spectrum and dispersion of Bogoliubov quasiparticles in two coupled elongated Bose-Einstein condensates. We develop an analytically solvable model that approximates two infinite homogeneous condensates and…
An efficient solver for the three dimensional free-space Poisson equation is presented. The underlying numerical method is based on finite Fourier series approximation. While the error of all involved approximations can be fully controlled,…