Gross pitaevskii equation solution
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 WebAug 11, 2016 · The Gross-Pitaevskii equation (GPE) is a successful and well-established model for describing an atomic Bose-Einstein condensate. Here we introduce this model, along with its assumptions. Throughout the rest of this chapter we explore its properties and key time-independent solutions. Keywords Harmonic Potential Trapping Potential …
Gross pitaevskii equation solution
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WebWe construct one soliton solutions for the nonlinear Schrödinger equation with variable quadratic Hamiltonians in a unified form by taking advantage of a complete (super) … WebJun 21, 2024 · The Gross–Pitaevskii equation is a widely accepted theoretical tool. High accuracy quantized-vortex solutions are desirable in many numerical and analytical …
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 … WebSep 19, 2006 · 356 Accesses 8 Citations Metrics We solve the time-independent Gross–Pitaevskii (GP) equation which describes the dilute Bose-condensed atoms in …
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 … WebMay 6, 2008 · Nonlinearity. We study the time-dependent Gross–Pitaevskii equation describing Bose–Einstein condensation of trapped dipolar quantum gases. Existence and uniqueness as well as the possible blow-up of solutions are studied. Moreover, we discuss the problem of dimension reduction for this nonlinear and nonlocal Schrödinger equation.
WebAbstract Quantized vortices are important topological excitations in Bose–Einstein condensates.The Gross–Pitaevskii equation is a widely accepted theoretical tool.High …
WebApr 3, 2024 · Specifically, the Gross–Pitaevskii (GP) equation was proposed in complex representation to obtain a pair of time-dependent equations, which were obtained in the real and imaginary parts, respectively. These equations were then discretized and solved based on the SPH particle approximation. boundary restaurant nashvilleWebWe construct one soliton solutions for the nonlinear Schrödinger equation with variable quadratic Hamiltonians in a unified form by taking advantage of a complete (super) integrability of generalized harmonic oscillato… boundary restaurant shoreditchWebJan 1, 2011 · Abstract and Figures. We present the application of finite difference method to solve the Gross-Pitaevskii equation in one dimension and timedependent. The solution method used is called Crank ... boundary retail parkWebApproximate 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… boundary retail park colneWebNov 1, 2024 · Abstract. This article deals with the stochastic Gross-Pitaevskii equation (SGPE) perturbed with multiplicative timenoise. The numerical solutions of the governing model are carried out with the proposed stochastic non … boundary retracementWebApr 30, 2024 · The Gross-Pitaevskii model is an extension of the Schrödinger equation, and it is given by [ 2, 3 ] where represents mass, is the interaction potential, and is the … boundary review 2022WebThis software is a CUDA-enabled non-linear Schrodinger (Gross-Pitaevskii) equation solver. The primary use of this code was for my research on rapidly rotating Bose-Einstein condensates. Due to the complexity and timescales needed to simulate such system, it was essential to write some accelerated code to understand the behaviour of such systems. boundary review