DeepAI AI Chat
Log In Sign Up

Modified discrete Laguerre polynomials for efficient computation of exponentially bounded Matsubara sums

01/05/2021
by   Guanpeng Xu, et al.
0

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) + ⋯ 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

08/14/2019

The sum-of-squares hierarchy on the sphere, and applications in quantum information theory

We consider the problem of maximizing a homogeneous polynomial on the un...
01/08/2023

A note on the rate of convergence of integration schemes for closed surfaces

In this paper, we issue an error analysis for integration over discrete ...
01/21/2020

Sparse Polynomial Interpolation Based on Diversification

We consider the problem of interpolating a sparse multivariate polynomia...
11/17/2021

Sharp Effective Finite-Field Nullstellensatz

The (weak) Nullstellensatz over finite fields says that if P_1,…,P_m are...
10/19/2021

Faster Rates for the Frank-Wolfe Algorithm Using Jacobi Polynomials

The Frank Wolfe algorithm (FW) is a popular projection-free alternative ...
09/25/2019

Temperature expressions and ergodicity of the Nosé-Hoover deterministic schemes

Thermostats are dynamic equations used to model thermodynamic variables ...