Results 11 to 20 of about 634 (180)
Exact analysis and elastic interaction of multi-soliton for a two-dimensional Gross-Pitaevskii equation in the Bose-Einstein condensation [PDF]
Journal of Advanced Research, 2022 Introduction: The Gross-Pitaevskii equation is a class of the nonlinear Schrödinger equation, whose exact solution, especially soliton solution, is proposed for understanding and studying Bose-Einstein condensate and some nonlinear phenomena occurring in
Haotian Wang, Qin Zhou, Wenjun Liu
doaj +4 more sources
Quantum Gross-Pitaevskii Equation [PDF]
SciPost Physics, 2017 We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of ...
Jutho Haegeman, Damian Draxler, Vid Stojevic, J. Ignacio Cirac, Tobias J. Osborne, Frank Verstraete
doaj +7 more sources
Complex soliton wave patterns of Gross–Pitaevskii systems: application in quantum and optical engineering [PDF]
Scientific ReportsThe purpose of this work is to explore precise solutions, particularly soliton solutions, by fractionally analyzing the multicomponent Gross–Pitaevskii problem, a basic nonlinear Schrödinger equation. Soliton solutions are essential for comprehending the
Muhammad Bilal +5 more
doaj +2 more sources
Superconvergence of time invariants for the Gross–Pitaevskii equation [PDF]
Mathematics of Computation, 2021 This paper considers the numerical treatment of the time-dependent Gross–Pitaevskii equation. In order to conserve the time invariants of the equation as accurately as possible, we propose a Crank–Nicolson-type time discretization that is combined with a suitable generalized finite element discretization in space.
Patrick Henning, Johan Wärnegård
openaire +2 more sources
Variational approach to multimode nonlinear optical fibers. [PDF]
NanophotonicsAbstract We analyze the spatiotemporal solitary waves of a graded‐index multimode optical fiber with a parabolic transverse index profile. Using the nonpolynomial Schrödinger equation approach, we derive an effective one‐dimensional Lagrangian associated with the Laguerre–Gauss modes with a generic radial mode number p and azimuthal index m.
Lorenzi F, Salasnich L.
europepmc +2 more sources
Quantitative Derivation of the Gross‐Pitaevskii Equation [PDF]
Communications on Pure and Applied Mathematics, 2014 Starting from first‐principle many‐body quantum dynamics, we show that the dynamics of Bose‐Einstein condensates can be approximated by the time‐dependent nonlinear Gross‐Pitaevskii equation, giving a bound on the rate of the convergence. Initial data are constructed on the bosonic Fock space applying an appropriate Bogoliubov transformation on a ...
Benedikter N, de Oliveira G, Schlein B
openaire +4 more sources
Results in Physics, 2023 This study applies computational and numerical techniques to develop some novel and accurate solutions for Gross–Pitaevskii (GP) equations. A quantum system of identical bosons is described using the Hartree–Fock approximation and pseudopotential ...
Mostafa M.A. Khater +3 more
doaj +1 more source
The inverse problem for the Gross–Pitaevskii equation [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2010 Two different methods are proposed for the generation of wide classes of exact solutions to the stationary Gross–Pitaevskii equation (GPE). The first method, suggested by the work of Kondrat’ev and Miller [Izv. Vyssh. Uchebn. Zaved., Radiofiz IX, 910 (1966)], applies to one-dimensional (1D) GPE.
Malomed, Boris A., Stepanyants, Yury A.
openaire +5 more sources
The stochastic Gross–Pitaevskii equation: II [PDF]
Journal of Physics B: Atomic, Molecular and Optical Physics, 2003 We provide a derivation of a more accurate version of the stochastic Gross-Pitaevskii equation, as introduced by Gardiner et al. (J. Phys. B 35,1555,(2002). The derivation does not rely on the concept of local energy and momentum conservation, and is based on a quasi-classical Wigner function representation of a "high temperature" master equation for a
Gardiner, C. W., Davis, M. J.
openaire +5 more sources
Stochastic projected Gross-Pitaevskii equation [PDF]
Physical Review A, 2012 We have achieved the first full implementation of the stochastic projected Gross-Pitaevskii equation for a three-dimensional trapped Bose gas at finite temperature. Our work advances previous applications of this theory, which have only included growth processes, by implementing number-conserving scattering processes. We evaluate an analytic expression
Rooney, S. J. +2 more
openaire +2 more sources