Mesoscopics in acoustics

The term mesoscopics has its origin in the electronics of small devices at low temperature. Ordinary electronics is well described by a picture of electrons as diffusing in an irregular geometry owing to scattering by impurities or rough surfaces or heterogeneous potentials. This picture of the electrons makes no reference to their wave nature. The electron wave is presumed incoherent and its phase irrelevant. In fact, though, the electron does have phase. But the phase is rendered incoherent by repeated scatterings in a time-varying medium, the time dependence being a consequence of thermally excited phonons or thermally excited other electrons. In the quantum literature such scattering is termed inelastic because scatterings that garble phase do not conserve the energy of the original electron. At low temperature, however, where there are few thermal excitations to scatter off, the lifetime of an electron against inelastic scattering can be longer than other relevant timescales. In this case the electron maintains a degree of phase coherence for a period long enough to be manifest macroscopically (or at least mesoscopically). Constructive and destructive interferences then lead to a variety of behaviors that can be nonintuitive to a theoretician operating within the simple diffusion picture. The regime is described by the inequality in which the mean free time against elastic scattering is short compared with the dwell time T of a wave in the sample before measurement (otherwise the field would be more propagative than diffuse), in turn much less than the time for phase garbling.