Abstract

We study the diffusion processes of a real scalar field in the presence of the distortion 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 with the diffusion flow and we discuss its main properties.

Graphic abstract

中文翻译：

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存在手性拓扑缺陷时的扩散

摘要

我们研究了在存在由手性拓扑缺陷引起的畸变场的情况下实标量场的扩散过程。该缺陷将通常的欧几里得背景几何修改为以奇异扭转场为特征的非对角黎曼-嘉当几何。建立了新形式的扩散方程，并对缺陷附近的标量场分布进行了数值研究。结果表明对边界条件的敏感性很高。在瞬态状态下，我们发现缺陷涡度产生与扩散流相关的角动量，我们讨论了它的主要性质。

图形摘要