SMS scnews item created by Andrew Mathas at Tue 5 Mar 2013 1409
Type: Seminar
Distribution: World
Expiry: 8 Mar 2013
Calendar1: 8 Mar 2013 1400-1500
CalLoc1: AGR Carslaw 829
CalTitle1: AGR Seminar: Complex dynamics and statistics of multidimensional Hamiltonian systems
Auth: mathas@pmathas.pc (assumed)

AGR Seminar

Complex dynamics and statistics of multidimensional Hamiltonian systems

Dr Tassos Bountis (University of Patras, Greece)

Host venue
La Trobe University

Abstract
Hamiltonian systems have been studied extensively by mathematicians and physicists for more than a century producing a wealth of theoretical results, which were later thoroughly explored by numerical and laboratory experiments. Especially in the case of few degrees of freedom, one might claim that most of their dynamical and statistical properties are well understood. And yet, in many dimensions, all the way to the thermodynamic limit, there remain many secrets to be revealed and surprising phenomena to be discovered. In this lecture, I will try to summarize the work I have been doing in the last few years with my team at Patras on complex problems of multidimensional Hamiltonian systems. I will first present the method of GALI indices to analyze the tangent space dynamics of individual orbits and explore some remarkable localization properties of one-dimensional lattices in configuration as well as Fourier space. In the second part of my talk, I will proceed more globally and study probability density functions (pdfs) of chaotic orbits in the spirit of the central limit theorem. In particular, I will demonstrate that weakly chaotic orbits often obey non-extensive statistical mechanics for long times, until they finally enter a regime of strong chaos, where pdfs tend to Gaussians, Boltzmann Gibbs theory prevails and the system tends to thermodynamic equilibrium. Recent applications to solid state physics and astronomy will be discussed.

Seminar convenor
Dr Yury Nikolayevsky

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If you would like to attend this seminar in our access grid room then please check to see if the grid is already booked at this time and send an email to accessgridroom@maths.usyd.edu.au to let the CSOs know that you would like to attend.


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