Numerical and Semiclassical Investigation OF Casimir energies and Forces

Rutgers University Newark, Newark NJ

Investigators

Abstract

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). Casimir effects are macroscopic manifestations of changes in the energy of the quantum ground state. They result from changes in boundary conditions or of classical backgrounds for quantized fields. The corresponding Casimir forces can dominate at micro- and nano-meter distances and in very strong gravitational fields. Building on the recently vastly improved understanding of such effects, this investigation will advance numerical and semi-classical estimates of Casimir energies and forces. World-line methods and algorithms are to be developed to the point that they permit the computation of Casimir forces in realistic systems with unprecedented accuracy. By directly generating convex surfaces with the appropriate probability measure very accurate vacuum forces could be obtained for a large class of convex bodies. The existing world-line formalism for calculating vacuum energies of scalar fields satisfying Dirichlet boundary conditions is to be extended to include other boundary conditions and ultimately compute vacuum forces due to quantum electrodynamics. The non-perturbative inclusion of effects due to surface roughness will also be investigated. Semi-classical methods will be used to analyze and guide the design of more efficient algorithms. Semi-classical periodic orbit theory will be further developed and applied to estimate changes in vacuum energy due to periodic classical photon orbits in the extreme space-times near (micro-) black holes and the early universe. The project introduces new analytic and computational methods to research in other fields as well. A well-defined stochastic measure on convex surfaces can be used to describe statistical deformations of higher dimensional convex spaces as well as of biological membranes. Stable micro black holes and Casimir effects due to extreme gravitational backgrounds could improve our understanding of dark matter and of dark energy. Accurate numerical estimates of Casimir forces in complex geometries furthermore will reduce development costs and improve the functionality of micro- and nano- mechanical devices. The control and efficient manipulation of vacuum forces is essential in the progressive miniaturization of mechanical devices. This project thus is at the heart of an emerging field of increasing technological importance. The project provides a post-doctoral associate the opportunity to contribute significantly to these developments. The activity is well-positioned to recruit and promote the work of under-represented minorities. It will ultimately have implications ranging from nanotechnology to cosmology.