Equidistribution of phase shifts in semiclassical potential scattering

Abstract

Consider a semiclassical Hamiltonian $H:=h^2\Delta +V-E$ where $\Delta$ is the positive Laplacian on ${\mathbb{R}}^d$, $V\in C_0^{\infty }({\mathbb{R}}^d)$ and $E>0$ is an energy level. We prove that under an appropriate dynamical hypothesis on the Hamilton flow corresponding to $H$, the eigenvalues of the scattering matrix $S_h(V)$ define a measure on ${\mathbb{S}}^1$ that converges to Lebesgue measure away from $1\in {\mathbb{S}}^1$ as $h\to 0$.

18 pages, 1 figure

References in corpus (3)

• The scattering matrix and associated formulas in Hamiltonian mechanics
• The spectral density of the scattering matrix for high energies
• Approximation and equidistribution of phase shifts: spherical symmetry

Cited by in corpus (1)

• Equidistribution of Phase Shifts in Obstacle Scattering