Recently the Casimir effect has been getting more popular because of its importance in designing micro and nano scale machines. Working in the language of quantum field theory simplified formulas for the Casimir energy for a massless scalar field are worked out. These formulas are applied to planar potentials and potentials in the annular region between two co-axial cylinders. A scalar equivalent to the Lifshitz formula is applied to new cases of non-trivial planar potentials, specifically two interacting linear potentials and two interacting quadratic potentials. In addition many exact expressions for the Casimir energy between two weakly coupled objects are worked out for many non-trivial geometries. Exact closed form results are shown for parallel cylinders, spheres, and finite ribbons and plates. These closed form results are used to check the range of validity of the proximity force approximation.
|Advisor:||Milton, Kimball A.|
|Commitee:||Baer, Howard, Baron, Eddie, Remling, Christian, Skubic, Pat|
|School:||The University of Oklahoma|
|Department:||Department of Physics and Astronomy|
|School Location:||United States -- Oklahoma|
|Source:||DAI-B 71/10, Dissertation Abstracts International|
|Keywords:||Casimir effect, Planar potentials, Vacuum fluctuations|
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