Quasi-equilibrium construction for long time glassy dynamics


Pierfrancesco Urbani (Università di Roma La Sapienza, Université Paris-Sud 11)


We present a quasi-equilibrium construction for long time glassy dynamics. This new method firstly clarifies how the dynamics explores the phase space when the dynamical glass transition is approached and secondly it gives a practical way to study the long time regime using equilibrium techniques. We will first review the quasi-equilibrium construction for a given class of mean field spin glass models that undergo a dynamical glass transition. For these systems the Langevin dynamics can be solved exactly and we can compare it with the dynamical equations obtained with the quasi-equilibrium construction. Because short time dynamics is coarse grained, equilibrium techniques and approximations can be used. We can apply this method to the theory of liquids and we will show how we can derive a set of new dynamical equations. In this framework we can use a standard approximation scheme, the Hypernetted Chain approximation (HNC), that has been racently employed to study the dynamical fluctuations in the β regime. We will derive the dynamical HNC equations from which we can compute both the exponent parameter that characterize glassy relaxation and the FDT-ratio in the aging regime. Our results can be generalized to any equilibrium closure scheme. The general picture is that long time Mode-Coupling dynamics can be interpreted as a quasi equilibrium exploration of phase space.

Designed by CSS.Design Sample