Propagation of singularities under Schrödinger equations on manifolds with ends

2022/01/24 by Shota Fukushima, Fukushima, Shota
Mathematics · Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Diffusion and Search Dynamics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2201.09466

Abstract

We prove a microlocal smoothing effect of Schrödinger equations on manifolds. We employ radially homogeneous wavefront sets introduced by Ito and Nakamura (Amer. J. Math., 2009). In terms of radially homogeneous wavefront sets, we can apply our theory to both of asymptotically conical and hyperbolic manifolds. We relate wavefront sets in initial states to radially homogeneous wavefront sets in states after a time development. We also prove a relation between radially homogeneous wavefront sets and homogeneous wavefront sets and prove a special case of Nakamura (2005).

Related

• Singularities of solutions to Schrodinger equation on scattering manifold
• Propagation of singularities for the wave equation on manifolds with corners
• Sharp local smoothing for manifolds with smooth inflection transmission
• Smoothing properties of dispersive equations on non-compact symmetric spaces
• Propagation of singularities for Schrödinger equations with modestly long range type potentials