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We present a numerical analysis of the single particle energy spectra of ballistic condensed matter systems and compare with recent theoretical results. We show that the presence even of weak disorder induces full chaoticity on time scales larger than the elastic disorder scattering time. To disentangle the effect of boundary, respectively disorder scattering on the spectral statistics, different types of correlation functions are introduced and discussed.

Information about the transport time of electrons through a quasi one-dimensional sample is obtained by calculating the energy auto-correlation function of the conductance. Depending on the length of the sample and its coupling to the external device (here modelled by perfectly conducting leads), the transport time undergoes a smooth crossover between two different limiting regimes. In the case of long samples and good coupling it coincides with the diffusion time. In the opposite limit of short and weakly coupled systems, however, the transport time is given by the reciprocal of the quantum mechanical decay width into the leads. The transition between both regimes is discussed in terms of a few model independent concepts.