<A HREF="https://aip.scitation.org/doi/abs/10.1063/1.4751279?crawler=true&journalCode=jmp">Growth of heat trace coefficients for locally symmetric spaces</A> [Journal of Mathematical Physics 53, 103506 (2012)] gives an application to quantum billiards.

> We study the asymptotic behavior of the heat trace coefficients for
> the scalar Laplacian in the context of locally symmetric spaces. These
> spaces have the distinguishing property that the Huygens principle for
> the shifted wave equation holds. As a consequence growth estimates
> conjectured by Berry and Howls [“*High orders of the Weyl expansion for
> quantum billiards: Resurgence of periodic orbits and the Stokes
> phenomenon*”] are sharp.