A systematic field theoretic description of the surface roughness corrections to the Casimir effect is developed. I use the multiple-scattering formalism. The Casimir energy is expressed in terms of the free Green's function and single-body scattering matrix. Finite temperature corrections to the Casimir force are obtained by Matsubara's formalism. The leading thermal corrections at high and low temperatures are presented and discussed. A statistical description of surface roughness is given and I construct the generating functional for roughness correlations. The latter allows me to incorporate roughness in a Quantum Field Theoretic (QFT) framework. I first consider a massless scalar field in the presence of parallel plates where one of which has a rough surface. In this case, semi-transparent boundary conditions are imposed by delta-function potentials. In the strong coupling limit the delta-function potential imposes Dirichlet boundary conditions. The Feynman rules of this equivalent 2+1-dimensional model are derived and its counterterms constructed. The two-loop contribution to the free energy of this model gives the leading roughness correction to the Casimir energy. The resummation of high-momentum loops shows that roughness effectively leads to a change in the mean separation of the order sigma^2/l_c and reduces reflection. The scalar model subsequently is generalized to the electromagnetic case. I derive the dielectric roughness corrections to the electromagnetic Casimir energy in a perturbative framework of the effective low-energy field theory for dielectric materials of Schwinger. It describes the interaction of electromagnetic fields with materials whose plasma frequency sets the low-energy scale. I show that the perturbative expansion of the single-interface scattering matrix in the amplitude of the profile is sensitive to short-wavelength components of the roughness correlation function. Generalized counterterms are introduced to subtract and correct these unphysical high-momentum contributions to the loop expansion. To leading perturbative order, the counterterms reproduce the phenomenological plasmon model. The renormalized low-energy theory is insensitive to the high-momentum behavior of the roughness correlation function and remains finite in the uncorrelated limit. I compare these predictions with the unrenormalized model and with experiment.
Subject (authority = ETD-LCSH)
Topic
Casimir effect
Subject (authority = RUETD)
Topic
Physics, Applied
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_5877
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
1 online resource (xxii, 133 p. : ill.)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = vita)
Includes vita
Subject (authority = ETD-LCSH)
Topic
Electromagnetic waves
Note (type = statement of responsibility)
by Hua-Yao Wu
RelatedItem (type = host)
TitleInfo
Title
Graduate School - Newark Electronic Theses and Dissertations
Identifier (type = local)
rucore10002600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
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