We develop a new type of orthogonal polynomial, the modified discrete Laguerre (MDL) polynomials, designed to accelerate the computation of bosonic Matsubara sums in statistical physics. The MDL polynomials lead to a rapidly convergent Gaussian "quadrature" scheme for Matsubara sums, and more generally for any sum $F(0)/2 + F(h) + F(2h) + \cdots$ of exponentially decaying summands $F(nh) = f(nh)e^{-nhs}$ where $hs>0$. We demonstrate this technique for computation of finite-temperature Casimir forces arising from quantum field theory, where evaluation of the summand $F$ requires expensive electromagnetic simulations. A key advantage of our scheme, compared to previous methods, is that the convergence rate is nearly independent of the spacing $h$ (proportional to the thermodynamic temperature). We also prove convergence for any polynomially decaying $F$.
翻译:我们开发了一种新型的正方形多面体,即经过修改的离散拉格瑞(MDL)多面体,旨在加速计算统计物理学中的松原体积。MDL多面体导致对松原体积的快速趋同性“二次曲线”方案,更一般地说,对于任何金额的松原体积,则需要为松原体积的“二次二次”+F(h)+F(2h)+F(2h)+\cdots$F(nh)=F(nh)=f(nh)e ⁇ -nhs}$0.0美元。我们演示了这种计算量场理论产生的有限温度卡西米尔力的技术,因为对美元和美元的评估需要昂贵的电磁模拟。与以往方法相比,我们的计划的一个主要优点是,趋同率几乎与美元间距(与热力温度成正比)几乎无关。我们也证明了任何多度衰减的美元的聚合。