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Dynamics of quantum hyperbolic Ruijsenaars-Schneider particles via diagonalization of analytic difference operators

Haworth, Steven William (2016) Dynamics of quantum hyperbolic Ruijsenaars-Schneider particles via diagonalization of analytic difference operators. PhD thesis, University of Leeds.

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Abstract

We present a new generalised eigenfunction of the reduced two-particle, mixed-charge, hyperbolic Ruijsenaars-Schneider (or, relativistic A_1-Calogero-Moser) Hamiltonian. The asymptotics of this function displays transmission and reflection in a way that generalizes the familiar non-relativistic picture. Using this function we construct integral transforms diagonalizing the Hamiltonian (an analytic difference operator, or A\DeltaO). When the three parametric dependences of the Hamiltonian are restricted to a certain polytope, these transforms can be used for a functional-analytic Hilbert space theory with all the desired quantum mechanical features (self-adjointness, spectrum, S-matrix etc.). As a final consideration we see how such a theory can be constructed in a different way for a special choice of the coupling parameter, with accompanying special features.

Item Type: Thesis (PhD)
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Keywords: Integrable systems, Ruijsenaars-Schneider model, Quantum mechanics, Transmission/reflection, Unbounded self-adjoint operators
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds)
Identification Number/EthosID: uk.bl.ethos.707062
Depositing User: Mr Steven William Haworth
Date Deposited: 03 Apr 2017 11:14
Last Modified: 25 Jul 2018 09:54
URI: http://etheses.whiterose.ac.uk/id/eprint/16801

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