A general spectral method for the numerical simulation of one-dimensional interacting fermions. (English) Zbl 1268.82021
Summary: This work introduces a general framework for the direct numerical simulation of systems of interacting fermions in one spatial dimension. The approach is based on a specially adapted nodal spectral Galerkin method, where the basis functions are constructed to obey the antisymmetry relations of fermionic wave functions. An efficient MATLAB program for the assembly of the stiffness and potential matrices is presented, which exploits the combinatorial structure of the sparsity pattern arising from this discretization to achieve optimal run-time complexity. This program allows for an accurate discretization of systems with multiple fermions subject to arbitrary potentials, e.g., for verifying the accuracy of multi-particle approximations such as Hartree-Fock in the few-particle limit. It can be used for eigenvalue computations or numerical solutions of the time-dependent Schrödinger equation.
MSC:
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 82-08 | Computational methods (statistical mechanics) (MSC2010) |
| 35Q41 | Time-dependent Schrödinger equations and Dirac equations |
| 82-04 | Software, source code, etc. for problems pertaining to statistical mechanics |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
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