Wave front set of solutions to the fractional Schr\"{o}dinger equation

In this paper, we characterize the wave front sets of solutions to fractional Schr\"{o}dinger equations $i\partial_{t}u =(-\Delta)^{\theta/2}u + V(x)u$ with $0<\theta <2$ via the wave packet transform (short-time Fourier transform). We clarify the relationship between the order $\theta$ of the fractional Laplacian and the growth rate of the potential in the problem of propagation of singularities. In particular, we present a theorem that bridges the propagation mechanisms of singularities for the Schr\"odinger and wave equations.