O ct 2 00 5 Ground - state structure and dynamics in a toy model for granular compaction

We report on a toy model for the glassy compaction dynamics of granular systems, introduced and investigated in collaboration with Anita Mehta and Peter Stadler. A stochastic dynamics is defined on a column of grains. Grains are anisotropic and possess a discrete orientational degree of freedom. Gravity induces long-range directional interactions down the column. The key control parameter of the model, ε, is a representation of granular shape. Rational and irrational values of ε correspond to very different kinds of behavior, both in statics (structure of ground states) and in low-temperature dynamics (retrieval of ground states). 1 Foreword In this contribution I have chosen to report on a series of works done in recent years in collaboration with Anita Mehta and Peter Stadler [1,2,3,4], where we have introduced and investigated in detail a columnar toy model for the com-paction dynamics of granular systems in the glassy regime. The main focus of this review is on the properties of this model which are of interest in the broader context of non-equilibrium dynamics and complex systems. We emphasize the relationship between statics (structure of ground states) and low-temperature dynamics (retrieval of these ground states). Surprisingly enough, some of the key features of this model belong to Serge Aubry's favorites, such as quasiperiodicity and hierarchical melting.