Spectral asymptotics of semiclassical unitary operators

Symplectic Spectral Geometry of Semiclassical Operators

In the past decade there has been a flurry of activity at the intersection of spectral theory and symplectic geometry. In this paper we review recent results on semiclassical spectral theory for commuting Berezin-Toeplitz and ~-pseudodifferential operators. The paper emphasizes the interplay between spectral theory of operators (quantum theory) and symplectic geometry of Hamiltonians (classical...

Semiclassical Spectral Invariants for Schrödinger Operators

In this article we show how to compute the semi-classical spectral measure associated with the Schrödinger operator on Rn, and, by examining the first few terms in the asymptotic expansion of this measure, obtain inverse spectral results in one and two dimensions. (In particular we show that for the Schrödinger operator on R2 with a radially symmetric electric potential, V , and magnetic potent...

Spectral asymptotics via the semiclassical Birkhoff normal form

This article gives a simple treatment of the quantum Birkhoff normal form for semiclassical pseudo-differential operators with smooth coefficients. The normal form is applied to describe the discrete spectrum in a generalised non-degenerate potential well, yielding uniform estimates in the energy E. This permits a detailed study of the spectrum in various asymptotic regions of the parameters (E...

Spectral Asymptotics of Laplace Operators on Surfaces with Cusps

Boundary spectral behaviour for semiclassical operators in one dimension

For a class of non-selfadjoint semiclassical operators in dimension one, we get a complete asymptotic description of all eigenvalues near a critical value of the leading symbol of the operator on the boundary of the pseudospectrum.