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Physics of Nonhermitian Degeneracies

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Czechoslovak Journal of Physics Aims and scope

Abstract

A summary, with references and additional comments, of a talk delivered at the Second International Workshop on Pseudohermitian Hamiltonians in Quantum Physics (Prague, 14-16 June 2004). After explaining some general features of nonhermitian degeneracies (‘exceptional points’), several applications are outlined: to multiple reflections in a pile of plates, linewidths of unstable lasers, atom diffraction by light, and crystal optics.

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References

  1. W. D. Heiss:Czech. J. Phys. 54 (2004)1091 (this issue).

    Google Scholar 

  2. T. Kato:Perturbation theory of linear operators,Springer, New York,1966.

    Google Scholar 

  3. M. V. Berry and M. Wilkinson:Diabolical points in the spectra of triangles,Proc. Roy. Soc. Lond. A 392 (1984)15–43.

    Google Scholar 

  4. M. V. Berry:Quantal phase factors accompanying adiabatic changes,Proc. Roy. Soc. Lond. A 392 (1984)45–57.

    Google Scholar 

  5. A. Shapere and F. Wilczek:Geometric Phases in Physics,World Scientific, Singapore,1989. 1046 Czech. J. Phys. 54 (2004).

    Google Scholar 

  6. H.-D. Dembowski, H.-D. Graf, H. L. Harney, A. Heine, W. D. Heiss, H. Rehfeld,and A. Richter:Experimental demonstration of he topological structure of exceptional points,Phys. Rev. Lett. 86(2001)787–790.

    Google Scholar 

  7. M. V. Berry and S. Klein:Transparent mirrors:rays,waves and localization,Eur. J. Phys. 18 (1997)222–228.

    Google Scholar 

  8. G. G. Stokes:On the intensity of the light reflected from or transmitted through a pile of plates,Proc. Roy. Soc. Lond. 11(1862)545–556.

    Google Scholar 

  9. M. V. Berry:Mode degeneracies and the Petermann excessnoise factor for unstable lasers,J. Mod. Opt. 50 (2003)63–81.

    Google Scholar 

  10. A. E. Siegman:Lasers,University Science Books, Mill Valley,1986.

    Google Scholar 

  11. M. V. Berry, C. Storm,and W. van Saarloos:Theory of unstable laser modes:edge waves and fractality,Opt. Commun. 197 (2001)393–402.

    Google Scholar 

  12. M. V. Berry:Fractal modes of unstable lasers with polygonal and circular mirrors,Opt. Commun. 200 (2001)321–330.

    Google Scholar 

  13. M. A. Yates and G. H. C. New:Fractal dimension of unstable resonator modes,Opt. Commun. 208 (2002)377–380.

    Google Scholar 

  14. G. H. C. New, M. A. Yates, J. P. Woerdman,and G. S. McDonald:Diffractive origin of fractal resonator modes,Opt. Commun. 193 (2001)261–266.

    Google Scholar 

  15. M. V. Berry and D. H. J. O 'Dell:Diffraction by volume gratings with imaginary potentials,J. Phys. A 31 (1998)2093–2101.

    Google Scholar 

  16. M. K. Oberthaler, R. Abfalterer, S. Bernet, J. Schmiedmayer,and A. Zeilinger:Atom waves in crystals of light,Phys. Rev. Lett. A 77 (1996)4980–4983.

    Google Scholar 

  17. M. V. Berry:Lop-sided difraction by absorbing crystals,J. Phys. A 31 (1998)3493–3502.

    Google Scholar 

  18. M. V. Berry and M. R. Dennis:The optical singularities of birefringent dichroic chiral crystals,Proc. Roy. Soc. A 459 (2003)1261–1292.

    Google Scholar 

  19. M. Born and E. Wolf:Principles of Optics,Pergamon, London,1959.

    Google Scholar 

  20. L. D. Landau, E. M. Lifshitz,and L. P. Pitaevskii:Electrodynamics of Continuous Media,Pergamon, Oxford,1984.

    Google Scholar 

  21. G. N. Ramachandran and S. Ramaseshan:Crystal Optics,Handbuch der Physik,Vol. XXV/I (Ed. H. Flügge),Springer-Verlag, Berlin,1961.

    Google Scholar 

  22. J. L. Synge:The Petrov classification of gravitational fields,Comm. Dubl. Inst. Adv. Stud.,ser. A 15 (1964)1–51.

    Google Scholar 

  23. W. D. Heiss and Harney:The chirality of exceptional points,Eur. Phys. J. D 17(1964) 149–151.

    Google Scholar 

  24. J. F. Nye and J. V. Hajnal:The wave structure of monochromatic electromagnetic radiation,Proc. Roy. Soc. Lond. A 409 (1987)21–36.

    Google Scholar 

  25. M. V. Berry and M. R. Dennis:Black polarization sandwiches are nontrivial square roo s of zero,J. OpticsA 6 (2004)S24-S25.

    Google Scholar 

  26. M. V. Berry, R. Bhandari,and S. Klein:Black plastic sandwiches demonstrating biaxial optical anisotropy,Eur. J. Phys. 20 (1999)1–14. Czech. J. Phys. 54 (2004)1047

    Google Scholar 

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Berry, M. Physics of Nonhermitian Degeneracies. Czechoslovak Journal of Physics 54, 1039–1047 (2004). https://doi.org/10.1023/B:CJOP.0000044002.05657.04

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