Abstract
The Casimir energy for the transverse oscillations of a piecewise uniform closed string is calculated. In its simplest version the string consists of two parts I and II having in general different tension and mass density, but is always obeying the condition that the velocity of sound is equal to the velocity of light. The model, first introduced by Brevik and Nielsen in 1990, possesses attractive formal properties implying that it becomes easily regularizable by several methods, the most powerful one being the contour integration method.We also consider the case where the string is divided into 2N pieces, of alternating type-I and type-II material. The free energy at finite temperature, as well as the Hagedorn temperature, are found. Finally, we make some remarks on the relationship between this kind of theory and the theory of quantum star graphs, recently considered by Fulling et al..
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Brevik, I., Nielsen, H. B.: Phys. Rev. D 41, 1185 (1990).
Li, X., Shi, X., Zhang, J.: Phys. Rev. D 44, 560 (1991).
Brevik, I., Elizalde, E.: Phys. Rev. D 49, 5319 (1994).
Elizalde, E.: Ten Physical Applications of Spectral Zeta Functions (Springer-Verlag, 1995),
Chapter 7.
Brevik, I., Nielsen, H. B.: Phys. Rev. D 51, 1869 (1995).
Brevik, I., Nielsen, H. B., Odintsov, S. D.: Phys. Rev. D 53, 3224 (1996).
Bayin, S. S., Krisch, J. P., Ozcan, M.: J. Math. Phys. 37, 3662 (1996).
Brevik, I., Sollie, R.: J. Math. Phys. 38, 2774 (1997).
Berntsen, M. H., Brevik, I., Odintsov, S. D.: Ann. Phys. (NY) 257, 84 (1997).
Brevik, I., Bytsenko, A. A., Nielsen, H. B.: Class. Quant. Grav. 15, 3383 (1998).
Brevik, I., Elizalde, E., Sollie, R., Aarseth, J. B.: J. Math. Phys. 40, 1127 (1999).
Brevik, I., Bytsenko, A. A., Pimentel, B. M. In: Theoretical Physics 2002, Part 2, p. 117. Eds.: George, T. F., Arnoldus, H. F. (Nova Sci. Publ., 2003).
Lu, J., Huang, B.: Phys. Rev. D 57, 5280 (1998).
Brevik, I., Bytsenko, A. A., Goncalves, A. E.: Phys. Lett. B 453, 217 (1999).
Brevik, I., Ellingsen, S. A˚ , Milton, K. A.: Phys. Rev. E 79, 041120 (2009).
Ellingsen, S. A˚ ., Brevik, I., Milton, K. A.: Phys. Rev. E 80, 021125 (2009).
Fulling, S. A., Kaplan, L., Wilson, J. H.: Phys. Rev. A 76, 012118 (2007).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Brevik, I. (2011). Casimir Effect for the Piecewise Uniform String. In: Odintsov, S., Sáez-Gómez, D., Xambó-Descamps, S. (eds) Cosmology, Quantum Vacuum and Zeta Functions. Springer Proceedings in Physics, vol 137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19760-4_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-19760-4_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19759-8
Online ISBN: 978-3-642-19760-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)