Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.298470
Title: Classical and quantum aspects of topological solitons (using numerical methods)
Author: Weidig, Tom
Awarding Body: Durham University
Current Institution: Durham University
Date of Award: 1999
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Abstract:
In Introduction, we review integrable and topological solitons. In Numerical Methods, we describe how to minimize functionals, time-integrate configurations and solve eigenvalue problems. We also present the Simulated Annealing scheme for minimisation in solitonic systems. In Classical Aspects, we analyse the effect of the potential term on the structure of minimal- energy solutions for any topological charge n. The simplest holomorphic baby Skyrme model has no known stable minimal-energy solution for n > 1. The one-vacuum baby Skyrme model possesses non-radially symmetric multi-skyrmions that look like 'skyrmion lattices' formed by skyrmions with n = 2. The two-vacua baby Skyrme model has radially symmetric multi- skyrmions. We implement Simulated Annealing and it works well for higher order terms. We find that the spatial part of the six-derivative term is zero. In Quantum Aspects, we find the first order quantum mass correction for the Ф(^4) kink using the semi-classical expansion. We derive a trace formula which gives the mass correction by using the eigenmodes and values of the soliton and vacuum perturbations. We show that the zero mode is the most important contribution. We compute the mass correction of Ф(^4) kink and Sine-Gordon numerically by solving the eigenvalue equations and substituting into the trace formula.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.298470  DOI: Not available
Keywords: SOLITONS; QUANTUM MECHANICS; CLASSICAL MECHANICS; TOPOLOGY; SKYRME POTENTIAL; CORRECTIONS; SINE-GORDON EQUATION; PHI4-FIELD THEORY; EIGENVALUES Physics Particles (Nuclear physics) Nuclear reactions Mathematics
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