Tapping of Granular Packs: A Model Based on Local Two-Level Systems

Two-level systems are known to be important for the low-temperature properties of glasses. We suggest here that they might explain some remarkable properties of powders under repeated tapping, as discovered by the Chicago group. Following the ideas of S. F. Edwards, the relevant variables here are (1) the volumes V(alpha) (V(beta)) occupied in the states alpha, beta (including distant reorganizations); (2) the magnitude B of the "activated volume" during a transition from alpha to beta; (3) the analog of temperatures, i.e., the compactivity (or free volume) v. Tapping induces alpha-->beta transitions, and these in turn reduce the compactivity. At low tapping strengths GammaGamma>Gamma(*)), the system freezes before reaching the alpha-beta equilibrium, and the density grows with the observed logarithmic law. At higher tapping strengths (Gamma