Spectrum of the d-bar Neumann Laplacian on the Fock space

The spectrum of the d-bar-Neumann Laplacian on the Fock space $L^2(\mathbb{C}^n, e^{-|z|^2})$ is explicitly computed. It turns out that it consists of positive integer eigenvalues each of which is of infinite multiplicity. Spectral analysis of the d-bar-Neumann Laplacian on the Fock space is closely related to Schr\"odinger operators with magnetic field and to the complex Witten-Laplacian.Comment: 8 page

XPS as a Probe of Gap Opening in Many Electron Systems

Core hole photoemission (XPS) provides a powerful indirect probe of the low energy excitations of a many electron system. We argue that XPS can be used to study the way in which a gap opens at a metal-superconductor or metal- insulator transition. We consider the "universal" physics of how the loss of low energy excitations modifies XPS spectra in the context of several simple models, considering in particular the case of a two dimensional d-wave superconductor.Comment: 8 pages, 9 eps figure