2018/12/31 by Péter Jeszenszki, Ali Alavi, Joachim Brand · 7 citations
Mathematics · Physics and Astronomy · #Advanced Frequency and Time Standards #Basis (linear algebra) #Basis function #Basis set #Cold Atom Physics and Bose-Einstein Condensates #Convergence (economics) #Fermion #Gaussian #Geometry #Mathematics #Physics #Pseudopotential #Quantum mechanics #Quantum, superfluid, helium dynamics #Range (aeronautics) #Scaling #Statistical physics #Wave function #cond-mat.quant-gas
paper · pdf · doi:10.1103/physreva.99.033608
published in Physical Review A 99(3) (American Physical Society) · 11 pages, 2 figures
openalex created_date 2018/12/22 · arxiv created 2019/03/06 · openalex publication_date 2019/03/11 · arxiv updated 2019/03/27 · openalex updated_date 2026/08/05
When seeking a numerical representation of a quantum-mechanical multiparticle problem it is tempting to replace a singular short-range interaction by a smooth finite-range pseudopotential. Finite basis set expansions, e.g., in Fock space, are then guaranteed to converge exponentially. The need to faithfully represent the artificial length scale of the pseudopotential, however, places a costly burden on the basis set. Here we discuss scaling relations for the required size of the basis set and demonstrate the basis set convergence on the example of a two-dimensional system of few fermions with short-range s-wave interactions in a harmonic trapping potential. In particular we show that the number of harmonic oscillator basis functions needed to reach a regime of exponential convergence for a Gaussian pseudopotential scales with the fourth power of the pseudopotential length scale, which can be improved to quadratic scaling when the basis functions are rescaled appropriately. Numerical examples for three fermions with up to a few hundred single-particle basis functions are presented and implications for the feasibility of accurate numerical multiparticle simulations of interacting ultracold-atom systems are discussed.