ABSTRACT
The idea of taking averages over all possible different states of a system is well understood and commonplace both in quantum mechanics and statistical physics. At finite temperatures, different possible states of a canonical ensemble, for exam ple, are occupied with Boltzmann probabilities, and observable physical properties are averages over the ensemble. Similarly, when we wish to measure a given phys ical observable in a quantum system, the result of the measurement is spread over different possible states with probabilities given by squared amplitudes of the wave function projection onto those states. During the last four decades consider able effort has gone into devising methods for carrying out averages of physical observables over different configurations realized by disordered systems. Why do we wish to carry out such averages and is such a procedure meaningful?
