Collaborative Research: The Casimir effect: Geometry and boundary condition dependence

Baylor University, Waco TX

Investigators

Abstract

This Collaborative Research is proposed by Klaus Kirsten, BaylorUniversity, and Paul Loya, Binghamton University. Casimir effect is a term used for quantum effects resulting from the finite extension of systems. The continuing miniaturization of technical devices makes this effect increasingly more important; e.g. in microelectromechanical systems it is responsible for up to 10% of the forces encountered. Also on cosmological scales this effect is relevant to the dark energy and to the stabilization of extra dimensions of the universe. However, presently not even the origin of the sign of the Casimir energy is well understood. In addition, the change of the Casimir energy is largely unknown when the shape of small objects and their material properties are altered. The goal of the present proposal is to considerably improve this situation by employing two completely different strategies. 1.) For highly symmetric situations, e.g. spheres, cubes and tori, the Casimir energy is well understood. Using contour integral methods this pool will be significantly increased to include configurations related to any separable coordinate system. 2.) At present, no practicable technique is known to find the change of the Casimir energy when the geometry of objects or their material properties are changed. This proposal entails a completely new approach. Analytical surgery, a geometric analysis method designed to analyze changes in spectral quantities, will be newly employed in the field of the Casimir effect. Broader Impacts. The deeper understanding of the Casimir effect is necessary for the optimal design of microelectromechanical devices. Furthermore this project will involve the collaboration of undergraduate and graduate students from various backgrounds and different departments. The techniques that the PIs will use to study the Casimir effect are accessible to advanced undergraduate students with a complex analysis background. An undergraduate text book and class on complex analysis, path integrals, and zeta regularized determinants will be developed by the PIs within the next two years. The newly established mathematical physics seminar at Baylor University started by Kirsten will serve to communicate results obtained under this grant to attract Baylor graduate students. Loya as the adviser of the Undergraduate Math Club at SUNY Binghamton will inform those students. This project will serve as a springboard to attract graduate students to this field of research to both involved universities. Finally, coming from the areas of mathematical physics (Kirsten) and analysis (Loya), the collaboration of the PIs in this project is multidisciplinary and will be a seed for new ideas combining physics and analysis.