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Monodromy in Hamiltonian systems

Pap, E.J. (2015) Monodromy in Hamiltonian systems. Bachelor's Thesis, Mathematics.

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Monodromy in Hamiltonian systems is the obstruction to the existence of globally defined smooth and single-valued action-angle variables. This subject in Hamiltonian mechanics has increased in attention in the past years. This thesis deals with an example system that exhibits monodromy; an idealized circularly symmetric microdisk with additional potential barrier inside. This system has billiard motion, and is proven to have monodromy in the fact that smooth and globally defined action variables need to be multi-valued. We find quantum monodromy in the quantum version confirmed by both the direct and WKB approximated spectra. Also an optical microresonator is investigated, but we see it has no monodromy unless a particular material can be made and used for it.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 08:05
Last Modified: 15 Feb 2018 08:05

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