A general spectral method for the numerical simulation of one-dimensional interacting fermions

Abstract 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 fr... Title of program: assembleFermiMatrix Catalogue Id: AEKO_v1_0 Nature of problem The direct numerical solution of the multi-particle one-dimensional Schrödinger equation in a quantum well is challenging due to the exponential growth in the number of degrees of freedom with increasing particles. Versions of this program held in the CPC repository in Mendeley Data AEKO_v1_0; assembleFermiMatrix; 10.1016/j.cpc.2011.10.005 AEKO_v1_1; assembleFermiMatrix; 10.1016/j.cpc.2012.03.015 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

摘要 本工作提出了一套用于一维空间内相互作用费米子系统直接数值模拟的通用框架。该方法依托经特殊适配的节点式谱Galerkin（spectral Galerkin）方法，其基函数的构建需严格遵循费米子波函数的反对称性关系。本文还给出了一款可高效组装刚度矩阵（stiffness matrix）与势能矩阵（potential matrix）的Matlab程序，该程序利用了由……产生的稀疏模式的组合结构（原文此处存在截断）。
程序标题：assembleFermiMatrix
目录编号：AEKO_v1_0
问题本质：针对量子阱（quantum well）中多粒子一维薛定谔方程（Schrödinger equation）的直接数值求解，由于自由度（degrees of freedom）数目随粒子数增加呈指数级增长，该问题极具挑战性。
存放在孟德莱数据（Mendeley Data）平台CPC库中的该程序版本：
AEKO_v1_0; assembleFermiMatrix; 10.1016/j.cpc.2011.10.005
AEKO_v1_1; assembleFermiMatrix; 10.1016/j.cpc.2012.03.015
本程序源自贝尔法斯特女王大学馆藏的CPC程序库（1969-2018年）