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arXiv · 1907.12676

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

Prakash Chakraborty·Bjorn Vermeersch·Ali Shakouri·Samy Tindel
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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.

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Prakash Chakraborty, Bjorn Vermeersch, Ali Shakouri, Samy Tindel. 2019-07-29. Relativistic stable processes in quasi-ballistic heat conduction in thin film semiconductors. https://doi.org/10.1103/physreve.101.042110

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