scispace - formally typeset
Search or ask a question
Topic

Gross–Pitaevskii equation

About: Gross–Pitaevskii equation is a research topic. Over the lifetime, 792 publications have been published within this topic receiving 15517 citations. The topic is also known as: Gross–Pitaevskii equation; GPE.


Papers
More filters
Journal ArticleDOI
TL;DR: In this article, the numerical solution of the time-dependent Gross-Pitaevskii equation (GPE) describing a Bose-Einstein condensate (BEC) at zero or very low temperature is studied.

525 citations

Journal ArticleDOI
TL;DR: Simple numerical algorithms for both stationary and non-stationary solutions of the time-dependent Gross–Pitaevskii (GP) equation describing the properties of Bose–Einstein condensates at ultra low temperatures are developed.

364 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that the k-particle density matrices of ψN,t are also asymptotically factorized and the one particle orbital wave function solves the Gross-Pitaevskii equation, a cubic nonlinear Schrodinger equation with the coupling constant given by the scattering length of the potential V.
Abstract: Consider a system of N bosons in three dimensions interacting via a repulsive short range pair potential N 2 V (N(xi − xj)), where x = (x1, . . ., xN) denotes the positions of the particles. Let HN denote the Hamiltonian of the system and let ψN,t be the solution to the Schrodinger equation. Suppose that the initial data ψN,0 satisfies the energy condition h ψN,0, H k N ψN,0i ≤ C k N k for k = 1,2, . . .. We also assume that the k-particle density matrices of the initial state are asymptotically factorized as N → ∞. We prove that the k-particle density matrices of ψN,t are also asymptotically factorized and the one particle orbital wave function solves the Gross- Pitaevskii equation, a cubic non-linear Schrodinger equation with the coupling constant given by the scattering length of the potential V. We also prove the same conclusion if the energy condition holds only for k = 1 but the factorization of ψN,0 is assumed in a stronger sense. AMS Subject Classification Number: 81V70, 81T18, 35Q55

344 citations

Journal ArticleDOI
TL;DR: The Gross-Pitaevskii equation is derived to describe droplets of such liquids and solved analytically in the one-dimensional case and shows that in the case of attractive inter- and repulsive intraspecies interactions the energy per particle has a minimum at a finite density corresponding to a liquid state.
Abstract: We calculate the energy of one- and two-dimensional weakly interacting Bose-Bose mixtures analytically in the Bogoliubov approximation and by using the diffusion Monte Carlo technique. We show that in the case of attractive inter- and repulsive intraspecies interactions the energy per particle has a minimum at a finite density corresponding to a liquid state. We derive the Gross-Pitaevskii equation to describe droplets of such liquids and solve it analytically in the one-dimensional case.

325 citations

Journal ArticleDOI
TL;DR: The nonlinear Schrodinger/Gross–Pitaevskii equation (NLSE/GPE) for modeling Bose–Einstein condensation (BEC) and nonlinear optics as well as other applications is discussed and their dynamical properties ranging from time reversible, time transverse invariant, mass and energy conservation, and dispersion relation to soliton solutions are discussed.

314 citations

Network Information
Related Topics (5)
Hamiltonian (quantum mechanics)
48.6K papers, 1M citations
81% related
Nonlinear system
208.1K papers, 4M citations
80% related
Eigenvalues and eigenvectors
51.7K papers, 1.1M citations
80% related
Quantum
60K papers, 1.2M citations
79% related
Quantum entanglement
39.5K papers, 1M citations
79% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202321
202251
202129
202039
201942
201841