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 本工作提出了一种面向一维空间相互作用费米子（fermions）系统的直接数值模拟通用框架。该方法依托经特殊适配的节点谱伽辽金法（nodal spectral Galerkin method），其基函数的构建需遵循费米子波函数的反对称性约束。本文还提供了一款高效的Matlab程序，用于组装刚度矩阵与势能矩阵，该程序充分利用了由……产生的稀疏模式的组合结构。 程序名称：assembleFermiMatrix 目录编号：AEKO_v1_0 问题本质 量子阱中的多粒子一维薛定谔方程（Schrödinger equation）直接数值求解难度较大，原因在于随着粒子数增加，系统自由度的数量呈指数级增长。 曼德利数据集（Mendeley Data）中的CPC库收录的该程序版本： 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《计算机物理学报》（Computer Physics Communications，简称CPC）程序库（1969-2018年）