International Journal of Theoretical Physics

, Volume 30, Issue 4, pp 531–536 | Cite as

Elliptically polarized fields and responses

  • ZhongJin Yang
  • Jie Yao
  • G. Helgesen
Article
  • 34 Downloads

Abstract

An ellipticaliy polarized field applied to a physical system and related responses are very common in physics. Due to the loss of symmetry, the response problems are very difficult to solve, and are usually described by nonlinear and unseparable equations. By introducing a time transformationτ=(1/ω)tan−1(r tanωt), wherer is the ratio between the two components, one may reset the symmetry of the field. The equation
$$\frac{{d\theta }}{{dt}} = \frac{{\omega r}}{{\cos ^2 \omega t + r^2 \sin ^2 \omega t}} - \omega _{\text{c}} (\cos ^2 \omega t + r^2 \sin ^2 \omega t)\sin {\text{2}}\theta $$
describing the relative angular motion of a magnetic dipole pair in an elliptical magnetic field has been solved with this transformation.

Keywords

Magnetic Field Field Theory Elementary Particle Quantum Field Theory Physical System 

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References

  1. Helgesen, G., Pieranski, P., and Skjeltorp, A. T. (1990).Physical Review Letters,64, 1425.Google Scholar
  2. Kamke, E. (1943).Differentialgleichungen, (Akademische Verlagsgesellschaft Becker & Erler Kom.-GES, Leipzig), pp. 21, 119, 121, and 410.Google Scholar
  3. Wang, Z. X., and Guo, D. R. (1965).Special Functions, Academic Press, Beijing, pp. 680 and 705 [in Chinese] [English translation: World Scientific, London (1989)].Google Scholar
  4. Watson, G. N. (1944).Theory of Bessel Functions, 2nd ed., Cambridge University Press, Cambridge, p. 92.Google Scholar
  5. Whittaker, E. T., and Watson, G. N. (1927).A Course of Modern Analysis, 4th ed., Cambridge University Press, Cambridge, p. 404.Google Scholar
  6. Yang, Z. J., and Yao, J. (1990).International Journal of Theoretical Physics,29, 1111.Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • ZhongJin Yang
    • 1
  • Jie Yao
    • 2
    • 3
  • G. Helgesen
    • 1
  1. 1.Department of PhysicsUniversity of OsloOslo 3Norway
  2. 2.University of OsloOslo 3Norway
  3. 3.International Center for Materials PhysicsAcademia SinicaShenyangChina

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