Scattering with real-time path integrals

TL;DR

This paper introduces a novel real-time path integral method to compute scattering matrix elements for short-range potentials, offering a new perspective on path integral interpretation and numerical implementation.

Contribution

It presents a new interpretation of the path integral as a potential functional expectation and demonstrates its numerical implementation for scattering calculations.

Findings

Successfully computes scattering matrix elements for Gaussian potentials.

Establishes a connection between the path integral approach and transfer matrix methods.

Provides a new computational framework for real-time scattering problems.

Abstract

Sharp-momentum transition matrix elements for scattering from a short-range Gaussian potential are computed using a real-time path integral. The computation is based on a numerical implementation of a new interpretation of the path integral as the expectation of a potential functional with respect to a complex probability distribution on cylinder sets of paths. The method is closely related to a unitary transfer matrix computation.