Bogoliubov treatment of the Gross–Pitaevskii equation is a method that finds the elementary excitations of a Bose–Einstein condensate. To that purpose, the condensate wavefunction is approximated by a sum of the equilibrium wavefunction and a small perturbation : See more The Gross–Pitaevskii equation (GPE, named after Eugene P. Gross and Lev Petrovich Pitaevskii ) describes the ground state of a quantum system of identical bosons using the Hartree–Fock approximation and … See more Since the Gross–Pitaevskii equation is a nonlinear partial differential equation, exact solutions are hard to come by. As a result, solutions have to be approximated via myriad techniques. Exact solutions Free particle See more • Trotter-Suzuki-MPI Trotter-Suzuki-MPI is a library for large-scale simulations based on the Trotter-Suzuki decomposition that can also address the Gross–Pitaevskii equation. • XMDS XMDS is a spectral partial differential equation library that can be used to solve the … See more The equation has the form of the Schrödinger equation with the addition of an interaction term. The coupling constant $${\displaystyle g}$$ is proportional to the s-wave scattering length $${\displaystyle a_{s}}$$ of two interacting bosons: See more The Gross-Pitaevskii equation can also be derived as the semi-classical limit of the many body theory of s-wave interacting identical bosons … See more • Pethick, C. J.; Smith, H. (2002). Bose–Einstein Condensation in Dilute Gases. Cambridge: Cambridge University Press. ISBN 978-0-521-66580-3. • Pitaevskii, L. P.; Stringari, S. (2003). Bose–Einstein Condensation. Oxford: Clarendon Press. ISBN See more WebApproximate solutions of the Gross-Pitaevskii (GP) equation, obtained upon neglection of the kinetic energy, are well known as Thomas-Fermi solutions. They are characterized by the compensation of the local potential b…
Exact soliton solutions of the generalized Gross …
WebApr 14, 2024 · 报告时间：2024年4月17日（星期一）10:00-11:00报告地点：翡翠湖校区科教楼B座1710室报 告 人：吴元泽 教授工作单位：中国矿业大学举办单位：数学学院报告简介：In this talk, I shall introduce our recent results on positive and spatially decaying solutions to the Gross-Pitaevskii equation with a harmonic potential, which give precisely ... WebSep 15, 2024 · Gross-Pitaevskii equation with NDSolve There are tips in that post on how to work with numerics of nonlinear PDEs. Your biggest missing point here is to apply cyclic (looped) boundary condition (non-lopped possible, … knot on lower back near spine
Numerical solution for the Gross–Pitaevskii equation
Web2 Gross-Pitaevskii equation At temperatures Tmuch smaller than the critical temperature T c[39], a BEC is well described by the macroscopic wave function ψ= ψ(x,t) whose … WebThe soliton is also a particular solution of the nonlinear Gross–Pitaevskii equation. Admittedly, the imprinted state is not the exact soliton solution. But it is close. The … WebAug 31, 2024 · The Gross–Pitaevskii equation is a non-linear Schrödinger equation with a cubic non-linearity: it describes the dynamics of Bose–Einstein condensates. Other … red fox snow