Classical fluctuations and semiclassical matrix elements

We discuss the fluctuation properties of diagonal matrix elements in the semiclassical limit in chaotic systems. For extended observables, covering a phase space area of many times Planck’s constant, both classical and quantal distributions are Gaussian. If the observable is a projection onto a single state or an incoherent projection onto several states classical and quantal distribution differ, but the mean and the variance are still obtainable from classical considerations.