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Numerical method for the projected Gross-Pitaevskii equation in an infinite rotating two-dimensional Bose gas

Lookup NU author(s): Dr Ryan DoranORCiD, Dr Thomas BillamORCiD

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Abstract

We present a method for evolving the projected Gross-Pitaevskii equation in an infinite rotating Bose-Einstein condensate, the ground state of which is a vortex lattice. We use quasiperiodic boundary conditions to investigate the behavior of the bulk superfluid in this system, in the absence of boundaries and edge effects. We also give the Landau gauge expression for the phase of a BEC subjected to these boundary conditions. Our spectral representation uses the eigenfunctions of the one-body Hamiltonian as basis functions. Since there is no known exact quadrature rule for these basis functions we approximately implement the projection associated with the energy cutoff, but we show that by choosing a suitably fine spatial grid the resulting error can be made negligible. We show how the convergence of this model is affected by simulation parameters such as the size of the spatial grid and the number of Landau levels. Adding dissipation, we use our method to find the lattice ground state for N vortices. We can then perturb the ground-state, to investigate the melting of the lattice.

Publication metadata

Author(s): Doran R, Billam TP

Publication type: Article

Publication status: Published

Journal: Physical Review E

Year: 2020

Volume: 102

Issue: 3

Online publication date: 11/09/2020

Acceptance date: 17/08/2020

ISSN (print): 1539-3755

ISSN (electronic): 1550-2376

Publisher: American Physical Society

URL: https://doi.org/10.1103/PhysRevE.102.033309

DOI: 10.1103/PhysRevE.102.033309

PubMed id: 33075866

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