PIRSA:09060000 Scientific Series

DOI10.48660/09060000

Series: Colloquium

Berry, M. (2009). Hamilton's diabolical singularity. Perimeter Institute. https://pirsa.org/09060000

Berry, Michael. Hamilton's diabolical singularity. Perimeter Institute, Jun. 03, 2009, https://pirsa.org/09060000 

@misc{ pirsa_PIRSA:09060000,
  doi = {10.48660/09060000},
  url = {https://pirsa.org/09060000},
  author = {Berry, Michael},
  keywords = {},
  language = {en},
  title = {Hamilton{\textquoteright}s diabolical singularity},
  publisher = {Perimeter Institute},
  year = {2009},
  month = {jun},
  note = {PIRSA:09060000 see, \url{https://pirsa.org}}
}

Abstract

The transformation of a narrow beam into a hollow cone when incident along the optic axis of a biaxial crystal, predicted by Hamilton in 1832, created a sensation when observed by Lloyd soon afterwards. It was the first application of his concept of phase space, and the prototype of the conical intersections and fermionic sign changes that now pervade physics and chemistry. But the fine structure of the bright cone contains many subtle features, slowly revealed by experiment, whose definitive explanation, involving new mathematical asymptotics, has been achieved only recently, along with definitive experimental test of the theory. Radically different phenomena arise when chirality and absorption are incorporated in addition to biaxiality.

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