This work presents an efficient numerical method to evaluate the free energy density and associated thermodynamic quantities of (quasi) one-dimensional classical systems, by combining the transfer operator approach with a numerical discretization of integral kernels using quadrature rules. For analytic kernels, the technique exhibits exponential convergence in the number of quadrature points. As demonstration, we apply the method to a classical particle chain, to the semiclassical nonlinear Schrödinger (NLS) equation and to a classical system on a cylindrical lattice. A comparison with molecular dynamics simulations performed for the NLS model shows very good agreement.

这项工作提出了一种有效的数值方法，通过将传递算子方法与使用正交规则的积分核的数值离散化相结合，来评估（准）一维经典系统的自由能密度和相关的热力学量。对于解析内核，该技术在正交点数量上表现出指数收敛性。作为演示，我们将该方法应用于经典粒子链，半经典非线性Schrödinger（NLS）方程以及圆柱晶格上的经典系统。与对NLS模型进行的分子动力学模拟的比较显示出很好的一致性。