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 published on a yearly basis
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.
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.
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
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.
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.
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