Abstract
We discuss the ordinary quantum Hall effect and a higher-dimensional cousin. We consider the dimensional reduction of these effects to 1 + 1 and 3 + 1 space-time dimensions, respectively. After dimensional reduction, an axion field appears, which plays the rôle of a space-time dependent difference of chemical potentials of chiral modes. As applications, we sketch a theory of quantum pumps and a mechanism for the generation of primeval magnetic fields in the early universe.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38, 1440 (1977). J. E. Kim, “Cosmic axion”, 2nd Intl. Workshop on Gravitation and Astrophysics, Univ. of Tokyo, 1997, astro-ph/9802061.
L. Saminadayar, D. C. Glattli, Y. Jin and B. Etienne, Phys. Rev. Lett. 79, 2526 (1997).
I.I. Tkachev, Sov. Astronom. Lett. 12, 305 (1986).
M. Turner and B. Widrow, Phys. Rev. D 37, 2743 (1988).
J. Fröhlich and B. Pedrini, in “Mathematical Physics 2000”, A. Fokas, A. Grigorian, T. Kibble and B. Zegarlinsky (eds.), Imperial College Press, London, 2000.
M. Joyce and M. Shaposhnikov, Phys. Rev. Lett. 79, 1193 (1997).
M. Giovannini, Phys. Rev. D 61, 063502 (2000). D. Grasso and H. R. Rubinstein, “Magnetic Fields in the Early Universe”, preprint astro-ph/0009061.
K. Von Klitzing, G. Dorda and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).
D. C. Tsui, H. L. Störnier and A. C. Gossard, Phys. Rev. B 48, 1559 (1982).
J. Fröhlich and T. Kerler, Nucl. Phys. B 354, 369 (1991).
S. Deser, R. Jackiw and S. Templeton, Ann. of Phys. 140, 372 (1982).
R. Jackiw, in “Current Algebras and Its Applications”, S. B. Treiman, R. Jackiw, D. J. Gross (eds.), Princeton University Press, Princeton NJ, 1972.
J. Fröhlich and E. Thiran, J. Stat. Phys. 76, 209 (1994). J. Fröhlich, U. M. Studer and E. Thiran, J. Stat. Phys. 86, 821 (1997).
J. Fröhlich, B. Pedrini, C. Schweigert and J. Walcher, J. Stat. Phys 103, 527 (2001).
B. J. van Wees et al., Phys. Rev. Lett. 60, 848 (1988).
A. J. Alekseev, V. V. Cheianov and J. Fröhlich, Phys. Rev. B 54, 320 (1996).
J. E. Avron, A. Elgart, G. M. Graf and L. Sadun, Phys. Rev. B 62, R10618 (2000), and Phys. Rev. Lett. 87, 236601 (2001).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Fröhlich, J., Pedrini, B. (2002). Axions, Quantum Mechanical Pumping, and Primeval Magnetic Fields. In: Cappelli, A., Mussardo, G. (eds) Statistical Field Theories. NATO Science Series, vol 73. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0514-2_26
Download citation
DOI: https://doi.org/10.1007/978-94-010-0514-2_26
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-0761-3
Online ISBN: 978-94-010-0514-2
eBook Packages: Springer Book Archive