Investigating the Spectral Geometry of a Soft Wall
Abstract
The idealized theory of quantum vacuum energy density is a beautiful application of the spectral theory of differential operators with boundary conditions, but its conclusions are physically unacceptable. A more plausible model of a reflecting boundary that stays within linear spectral theory confines the waves by a steeply rising potential function, which can be taken as a power of one coordinate, z^\alpha. We report investigations of this model with considerable student involvement. An exact analytical solution with some numerics for \alpha=1 and an asymptotic (semiclassical) analysis of a related problem for \alpha=2 are presented.
Keywords
Cite
@article{arxiv.1106.1162,
title = {Investigating the Spectral Geometry of a Soft Wall},
author = {J. D. Bouas and S. A. Fulling and F. D. Mera and K. Thapa and C. S. Trendafilova and J. Wagner},
journal= {arXiv preprint arXiv:1106.1162},
year = {2012}
}
Comments
16 pages,4 figures; International Conference on Spectral Geometry (Dartmouth, 2010). Revision (final submission to Proc. Symp. Pure Math.) has minor updates and corrections