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Title: Casimir theory for the piecewise uniform string: Division into 2[ital N] pieces

Journal Article · · Physical Review, D (Particles Fields); (United States)
 [1];  [2]
  1. Applied Mechanics, The Norwegian Institute of Technology, N-7034 Trondheim (Norway)
  2. The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen O (Denmark)

The Casimir energy for the transverse oscillations of a piecewise uniform string in Minkowski space is calculated. The string consists in general of 2[ital N] pieces of equal length, of alternating type I and type II material, endowed with different tensions [ital T][sub I], [ital T][sub II] and mass densities [rho][sub I], [rho][sub II] but adjusted in such a way that the velocity of sound always equals the velocity of light. This string model (with [ital N]=1) was introduced by the present authors in 1990. In the present paper, the governing equations are formulated in the case of arbitrary integers [ital N], although detailed calculations are restricted to the case [ital N]=2, i.e., a four-piece string. The Casimir energy is regularized using (i) the contour integration technique introduced by van Kampen, Nijboer, and Schram, and (ii) the Hurwitz [zeta]-function technique introduced by Li, Shi, and Zhang. The energy is found as a function of the tension ratio [ital x]=[ital T][sub I]/[ital T][sub II]. The finite temperature version of the theory is also given.

OSTI ID:
6580904
Journal Information:
Physical Review, D (Particles Fields); (United States), Vol. 51:4; ISSN 0556-2821
Country of Publication:
United States
Language:
English