Relativistic stable processes in quasiballistic heat conduction in semiconductors.

In this article, we show how relativistic a-stable processes can be used to explain quasiballistic 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 the Feynman-Kac formalism and random processes that transition from a stable Levy process on short time and length scales to the Brownian motion at larger scales. This transition was captured by a heuristic truncated Levy distribution in earlier papers. The rigorous Feynman-Kac approach is used to derive sharp bounds for the transition kernel. Future directions are briefly discussed.