# Relativistic stable processes in quasi-ballistic heat conduction in thin film semiconductors

## TL;DR

This paper introduces a relativistic alpha stable process model to explain quasi-ballistic heat conduction in thin semiconductor films, connecting experimental ultrafast laser heating results with advanced stochastic process theory.

## Contribution

It applies relativistic alpha stable processes and Feynman-Kac formalism to model heat conduction, bridging short-scale Levy processes and large-scale Brownian motion.

## Key findings

- Model fits experimental ultrafast laser heating data
- Derives sharp bounds for transition kernels using Feynman-Kac formalism
- Establishes a theoretical connection between Levy processes and Brownian motion

## Abstract

In this article, we show how relativistic alpha stable processes can be used to explain quasi-ballistic heat conduction in semiconductors. This is a method that can fit experimental results of ultrafast laser heating in alloys. It also provides a connection to a rich literature on Feynman-Kac formalism and random processes that transition from a stable L\'evy process on short time and length scales to the Brownian motion at larger scales. This transition was captured by a heuristic truncated L\'evy distribution in earlier papers. The rigorous Feynman-Kac approach is used to derive sharp bounds for the transition kernel. Future directions are briefly discussed.