Tunneling of a Massless Field through a 3D Gaussian Barrier

TL;DR

This paper introduces a method to approximate the Green function of a massless scalar field interacting with a 3D Gaussian barrier, focusing on tunneling effects and potential energy corrections between sources.

Contribution

It presents a novel approximation technique for the Green function in the presence of complex potential barriers, specifically applied to a 3D Gaussian shape.

Findings

Numerical evaluation of potential correction varies with barrier size.

Tunneling effects significantly influence the static potential energy.

Method provides insights into quantum tunneling in curved spacetime barriers.

Abstract

We propose a method for the approximate computation of the Green function of a scalar massless field Phi subjected to potential barriers of given size and shape in spacetime. This technique is applied to the case of a 3D gaussian ellipsoid-like barrier, placed on the axis between two pointlike sources of the field. Instead of the Green function we compute its temporal integral, that gives the static potential energy of the interaction of the two sources. Such interaction takes place in part by tunneling of the quanta of Phi across the barrier. We evaluate numerically the correction to the potential in dependence on the size of the barrier and on the barrier-sources distance.