EQUIDISTRIBUTION OF PHASE SHIFTS IN SEMICLASSICAL POTENTIAL SCATTERING

Abstract. Consider a semiclassical Hamiltonian H: = h2 ∆ + V − E where ∆ is the positive Laplacian on Rd, V ∈ C∞0 (Rd) 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 Sh(V) define a measure on S1 that converges to Lebesgue measure away from 1 ∈ S1 as h → 0. 1.