[fod] Fesitval of Doubt: 30/5/02.

[Marcus Gallagher <marcusg@itee.uq.edu.au>]

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Festival of Doubt
http://festivalofdoubt.uq.edu.au
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Date: Thursday, 30th May
Time: 4pm
Place: 78-224 (GPSouth Building)

Speaker: Ben Skellett
Title: Classical Dynamics of Magnetically Coupled Spins

Abstract:

The dynamics of a nonintegrable coupled two-spin system are
investigated.  This Hamiltonian system is a model for two magnetic
molecules coupled via a particular nonlinear interaction.  A model
like this has been proposed as a realisation for quantum bits in
quantum computing.

A critical value of the coupling parameter is identified.  Below
this critical value, motion is approximately regular and the system
is robust to weak coupling.  At the critical value the system
undergoes a supercritical pitchfork bifurcation and motion can
subsequently be localised about the additional elliptic fixed
points.  The localised motion is typically regular, though for less
extreme energy values an extensive chaotic region leads to
unpredictable behaviour.  The energy of the system plays a crucial
role in determining the accessible regions of the phase space and
the behaviour of the system.

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This presentation will include many colourful pictures of 4
dimensional energy surfaces, chaotic Poincare maps and a dynamic
Matlab simulation of the spins.  All concepts will be explained,
leaving out most of the scary maths.  The emphasis is on modelling
the system and using mathematical and numerical analysis to
understand the dynamics.

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marcusg@itee.uq.edu.au http://www.itee.uq.edu.au/~marcusg/