Numerical path integration with Coulomb potential

Local representation of N-body Coulomb energy with path integrals

We represent N-body Coulomb energy in a localized form to achieve massive parallelism. It is a well-known fact that Green's functions can be written as path integrals of field theory. Since two-body Coulomb potential is a Green's function of Poisson equations, it reduces to a path integral of free scalar field theory with three spatial dimensions. This means that N-body one also reduces to a path integral. We discretize real space with a cubic lattice and evaluate the obtained multiple integrals approximately with the Markov-chain Monte Carlo method.

Numerical integration for ab initio many-electron self energy calculations within the GW approximation

We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite …

Quantum Monte Carlo Method for Attractive Coulomb Potentials

Starting from an exact lower bound on the imaginary-time propagator, we present a Path-Integral Quantum Monte Carlo method that can handle singular attractive potentials. We illustrate the basic ideas of this Quantum Monte Carlo algorithm by simulating the ground state of hydrogen and helium.

Path-accelerated molecular dynamics: Parallel-in-time integration using path integrals

Massively parallel computer architectures create new opportunities for the performance of long-timescale molecular dynamics (MD) simulations. Here, we introduce the path-accelerated molecular dynamics (PAMD) method that takes advantage of distributed computing to reduce the wall-clock time of MD simulation via parallelization with respect to MD timesteps. The marginal distribution for the time evolution of a system is expressed in terms of a path integral, enabling the use of path sampling techniques to numerically integrate MD trajectories. By parallelizing the evaluation of the path action w…

On the numerical evaluation of real-time path integrals: Double exponential integration and the Maslov correction

Ooura's double exponential integration formula for Fourier transforms is applied to the oscillatory integrals occuring in the path-integral description of real-time Quantum Mechanics. Due to an inherent, implicit regularization multi-dimensional Gauss-Fresnel integrals are obtained numerically with high precision but modest number of function calls. In addition, the Maslov correction for the harmonic oscillator is evaluated numerically with an increasing number of time slices in the path integral thereby clearly demonstrating that the real-time propagator acquires an additional phase $ - π/2 $…

COLOSS：复标度光学与库仑散射求解器

COLOSS: Complex-scaled Optical and couLOmb Scattering Solver

COLOSS程序利用复标度束缚态技术解决散射问题，通过将波函数振荡边界条件转化为指数衰减条件来处理长程库仑相互作用，支持计算S-矩阵和截面，并在精度上优于直接积分法Numerov。