Spectral functions for generalized piston configurations.

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dc.contributor.advisor Kirsten, Klaus, 1962- Morales-Almazán, Pedro Fernando. 2012-08
dc.description.abstract In this work we explore various piston configurations with different types of potentials. We analyze Laplace-type operators P=-g^ij ∇^E_i ∇ ^E_j+V where V is the potential. First we study delta potentials and rectangular potentials as examples of non-smooth potentials and find the spectral zeta functions for these piston configurations on manifolds I x N, where I is an interval and N is a smooth compact Riemannian d-1 dimensional manifold. Then we consider the case of any smooth potential with a compact support and develop a method to find spectral functions by finding the asymptotic behavior of the characteristic function of the eigenvalues for P. By means of the spectral zeta function on these various configurations, we obtain the Casimir force and the one-loop effective action for these systems as the values at s= -½ and the derivative at s = 0. Information about the heat kernel coefficients can also be found in the spectral zeta function in the form of residues, which provide an indirect way of finding this geometric information about the manifold and the operator. en_US
dc.publisher en
dc.rights Baylor University theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact for inquiries about permission. en_US
dc.subject Spectral functions. en_US
dc.subject Casimir effect. en_US
dc.title Spectral functions for generalized piston configurations. en_US
dc.type Thesis en_US Ph.D. en_US
dc.rights.accessrights Worldwide access en_US
dc.contributor.department Mathematics. en_US
dc.contributor.schools Baylor University. Dept. of Mathematics. en_US

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