Diffusion in the presence of a chiral topological defect

TL;DR

This paper investigates how a chiral topological defect alters diffusion processes of a scalar field within a non-diagonal Riemann-Cartan geometry, revealing defect-induced angular momentum and sensitivity to boundary conditions.

Contribution

It introduces a new diffusion equation in a non-diagonal geometry with a chiral defect and analyzes the defect's impact on scalar field distribution and flow properties.

Findings

Diffusion is highly sensitive to boundary conditions near the defect.

The defect's vorticity induces angular momentum in the diffusion flow.

Numerical analysis reveals unique distribution patterns around the defect.

Abstract

We study the diffusion processes of a real scalar field in the presence of the distorsion field induced by a chiral topological defect. The defect modifies the usual Euclidean background geometry into a non-diagonal Riemann-Cartan geometry characterized by a singular torsion field. The new form of the diffusion equation is established and the scalar field distribution in the vicinity of the defect is investigated numerically. Results show a high sensitivity to the boundary conditions. In the transient regime, we find that the defect vorticity generates an angular momentum associated to the diffusion flow and we discuss its main properties.