An orthonormal gradient flow for computing ground state solution of two-dimensional dipolar fermion gas

• Published in: Advances in computational mathematics Vol. 51; no. 4
• Main Authors: Zhang, Xuelin, Wang, Hanquan
• Format: Journal Article
• Language: English
• Published: New York Springer Nature B.V 01.08.2025
• Subjects: Density functional theory; Fermions; Gradient flow; Ground state; Numerical methods; Partial differential equations; Spectral methods
• ISSN: 1019-7168; 1572-9044
• DOI: 10.1007/s10444-025-10248-6

In this paper, based on density functional theory, we present an orthonormal gradient flow (OGF) for finding the ground state solution of a two-dimensional dipolar fermion gas. The OGF has the properties of orthonormality preserving and energy diminishing. By evolving such OGF, we may get the ground state solution of the dipolar fermion gas numerically. The OGF consists of time-dependent integral and partial differential equations. In principle, it can be discretized with many kinds of numerical techniques. We propose a backward Euler Fourier spectral method to discretize such OGF numerically. Numerical tests are reported to demonstrate the effectiveness of the proposed methods. The proposed numerical methods are applied to compute the ground state solution of the ultracold dipolar fermion gas.