Non-equilibrium statistical mechanics applied to glassy systems

The glass transition in an interesting unsolved problem in statistical mechanics. Over the last two decades our understanding of both the glass transition and of nonequilibrium statistical mechanics has been improved by the use of molecular dynamics simulation (MD). A glassy system fails to relax to equilibrium after having its temperature reduced dramatically, from an initial equilibrium state, even after waiting for very long times. A non-equilibrium MD simulation is constantly driven, by an external field, with the energy being dissipated as heat via a thermostat. Typically a simulation of a glassy system requires very long time scales to be computed while non- equillibrium MD requires the simulation to be repeated a large number of times over a much shorter time scale. Until very recently the prospect of combining these two types of simulations was not feasible, however with current state of the art computer power this can be achieved, which will allow some of the theoretical formalism of non- equilibrium statistical mechanics to be applied to glassy systems for the first time.

Principal Investigator

Stephen Williams
Physical and Theoretical Chemistry, RSC
Australian National University

Project

h57

Co-Investigators

Denis Evans
Alan Wouterse
Physical and Theoretical Chemistry, RSC
Australian National University

RFCD Codes

250602

Significant Achievements, Anticipated Outcomes and Future Work

Considerable progress has been achieved towards completing the aims set out in the original project description. The work described in paragraph b) of the original proposal has been completed for the specific case of a single particle interacting with a constant external dissipative force. Using the APAC facilities we have shown that the steady state fluctuation theorem converges on a time, which diverges as the glass transition is approached. This implies that the maximum external dissipative field strength for which a steady state linear response may be observed shrinks to zero as the glass transition is approached. By performing a large number of simulations we have shown how this field strength scales with the diffusion coefficient as the glass transition temperature is approached. The behaviour of the diffusion coefficient upon approaching the glass transition is well understood from numerous studies carried out by others. This gives fundamental new insight into the glass transition. At temperatures above the glass transition a linear response may be observed for a small dissipative external field. Below the glass transition the response is intrinsically nonlinear and a very small dissipative field may be supported in a manner typically associated with a solid. The fact that very small field strengths are necessary to observe a linear response in the vicinity of the glass transition has required the simulations to be repeated a large number of times to obtain statistically meaningful results. We could not have done this work without the support from APAC. A paper on this work is currently under review in the journal Physical Review Letters. We intend to repeat this work for the case of stress controlled planner shear. The work described in paragraph a) is on going. Thus far we have shown that the fluctuation theorem works in glasses along with a number of other results drawn from statistical mechanics, which assume an equilibrium Boltzmann distribution. This work is leading towards a pedagogical description of how the glassy state may be effectively described by equilibrium distribution functions restricted to local domains.

 

Computational Techniques Used

Molecular Dynamics Simulation

 

Publications, Awards and External Funding

External Funding and Awards

ARC DP0449810, DP0342706

Publications

S. R. Williams and D. J. Evans, Linear Response Domain in Glassy Systems, Physical Review Letters, 96, 2006, 015701-1 015701-4
S. R. Williams, G. Bryant, I. K. Snook and W. van Megen, Velocity Autocorrelation Functions of Hard-Sphere Fluids: Long-Time Tails upon Undercooling, Physical Review Letters, 96, 2006, 087801-1 087801-4
S. R. Williams, D. J. Searles and D. J. Evans, Numerical study of the steady state fluctuation relations far from equilibrium, Journal of Chemical Physics, In Press.