In statistical physics one is trained to think about the properties of large ensembles of particles, and to calculate bulk properties by averaging over many microscopic configurations. Although the quantum mechanical properties of the individual constituents of a macroscopic object are important over some length scale (typically a few lattice spacings), they are usually not correlated across the whole object. We are, however, becoming acquainted with more and more disordered systems for which this effective length scale, at low temperatures, can be 100–10 000 times the characteristic microscopic scale; the correlation can involve more than particles. Such phenomena occur in an intermediate “mesoscopic” regime that lies between the microscopic world of atomic and molecular orbitals and the thoroughly macroscopic world where averages tell all. The wealth of novel quantum coherence phenomena recently observed in this intermediate size regime is the subject of this article.
Phase coherence over thousands of lattice spacings in disordered metals can produce quantum interference effects in electrical resistance measured in very small devices.