Tapping of granular packs: A model based on local two-level systems

Two-level systems are known to be important for the low-temperature propert ies of glasses. We suggest here that they might explain some remarkable pro perties of powders under repeated tapping, as discovered by the Chicago gro up. 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 (includi ng 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) nu. Tapping induces alpha --> beta tra nsitions, and these in turn reduce the compactivity. At low tapping strengt hs Gamma (Gamma < Gamma*), the system freezes before reaching the alpha-bet a equilibrium, and the density grows with the observed logarithmic law. At higher tapping strengths (Gamma > Gamma*) the beta<->beta equilibrium may b e approached and competes with freezing (because the free volume is expecte d to increase with Gamma). The scenarios are discussed here for two limits; (a) a well-defined difference Delta = V-alpha - V-beta,(b) a flat distribu tion of Delta values, which gives rather different predictions. (C) 2000 Ac ademic Press.