Dynamical Systems Seminar: Juan Restrepo

Stabilization of incoherence in the disordered Hamiltonian Mean Field model

Juan Restrepo

Applied Mathematics, University of Colorado Boulder

Date and time: 

Thursday, October 17, 2013 - 2:00pm

Location: 

ECCR 257

Abstract: 

We study the Hamiltonian Mean Field model of coupled Hamiltonian rotors with a heterogeneous distribution of moments of inertia and coupling strengths. We show that when the parameters of the rotors are heterogeneous, finite size fluctuations can greatly modify the coupling strength at which the incoherent state loses stability by inducing correlations between the momentum and parameters of the rotors. For unimodal parameter distributions, we find an analytical expression for the modified critical coupling strength in terms of statistical properties of the parameter distributions and confirm our results with numerical simulations. We find numerically that these effects disappear for strongly bimodal parameter distributions.