Reversible and irreversible dynamics in a sheared Wigner crystal
- Event time: 4:00pm
- Event date: 7th January 2014
- Speaker: Bruno Eckhart (Philipps-Universität Marburg)
- Location: Room 2511, James Clerk Maxwell Building (JCMB) James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD GB
Experiments by Pine et al  have revealed a transition between reversible and irreversible motion in a many body system. They studied the dynamics of a suspension of spherical glass beads in a viscous liquid under oscillatory shear. When the shear amplitude is small, almost all particles return to their initial position, but when the shear amplitude exceeds a critical threshold the particles do not return to their initial positions and show a diffusive behaviour with a diffusion constant that increases with shear amplitude. The behaviour was rationalized in a statistical model for the particle-shear interaction .
In order to connect this behaviour to the reversibility and exponential instability in dynamical systems  we study the over-damped dynamics of a 2-d system of repulsively interacting particles. For equal particles the stationary equilibrium configuration is a tetragonal lattice. Under shear this lattice develops an instability for a range of frequencies and shear amplitudes.
The diffusive motion of the particles requires that neighbouring particles exchange positions. We use edge tracking  to identify the transition states for such processes. The states are exponentially localized and cover about 5x5 particles in 2-d.
 D. J. Pine, J. P. Gollub, J. F. Brady, and A. M. Leshansky, Nature 438, 997 (2005)  L. Corte, P.M. Chaikin, J.P. Gollub, and D.J. Pine, Nature Physics 4, 420 (2008).  B. Eckhardt, J. Phys. A 36, 371-380 (2003).  J. Skufca, B. Eckhardt and J.A. Yorke, Phys Rev Lett 96, 174101 (2006).
This is a weekly series of informal talks given primarily by members of the soft condensed matter and statistical mechanics groups, but is also open to members of other groups and external visitors. The aim of the series is to promote discussion and learning of various topics at a level suitable to the broad background of the group. Everyone is welcome to attend..