EIGENVALUE STATISTICS OF DISORDERED CONDUCTORS

We apply the statistical measures of Wigner, Dyson and Mehta to quantum-mechanical systems having intrinsic disorder. We observe a transition from regular Poisson-like to Wigner-like eigenvalue statistics, and relate these two limiting behaviours to the ballistic and mesoscopic regimes of quantum transport. In strongly disordered systems we observe that the eigenvalue spectra have a more complex structure, whose nature seems to provide a useful indicator of transport behaviour. We also observe similar effects in the spectra of quantum-mechanical systems whose classical analogues exhibit chaotic behaviour, and we can therefore provide a semi-quantitative description of the non-universal conductance fluctuations recently observed by Marcus and co-workers in ballistic microstructures.