2020/02/29 by R. Doran, T. P. Billam · 1 citation
Mathematics · Physics and Astronomy · #Bose gas #Bose–Einstein condensate #Boundary value problem #Cold Atom Physics and Bose-Einstein Condensates #Eigenfunction #Eigenvalues and eigenvectors #Gross–Pitaevskii equation #Ground state #Hamiltonian (control theory) #Lattice (music) #Mathematical analysis #Mathematics #Mechanics #Periodic boundary conditions #Physics #Physics of Superconductivity and Magnetism #Projection method #Quantum mechanics #Strong Light-Matter Interactions #Superfluidity #Vortex #cond-mat.quant-gas
paper · pdf · doi:10.1103/physreve.102.033309
published as Phys. Rev. E 102, 033309 (2020) · Version 2, updated 3rd September 2020. 14 pages, 8 figures
arxiv created 2020/09/03 · openalex publication_date 2020/09/11 · arxiv updated 2020/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.