EVOLUTION OF A VIBRATIONAL WAVE-PACKET ON A DISORDERED CHAIN

A linear chain of point masses coupled by harmonic springs is a standa rd model used to introduce concepts of solid state physics. The well-o rdered chain has sinusoidal standing wave normal modes (if the ends ar e fixed) or traveling wave normal modes (if the ends are connected in a ring). Ballistically propagating wave packets can be built from thes e normal modes, and illustrate the mechanism of heat propagation in in sulating crystals. When the chain is disordered, new effects arise. Ba llistic propagation is replaced by diffusive propagation on length sca les larger than the mean free path for ballistic motion. However, a ne w length scale, the localization length, also enters. On length scales longer than the localization length, neither ballistic nor diffusive propagation occurs, and energy is trapped unless there are anharmonic forces. These ideas are illustrated by a computer experiment. (C) 1998 American Association of Physics Teachers.