Statistical Description of Eigenfunctions in Chaotic and Weakly Disordered Systems beyond Universality

We present a semiclassical approach to eigenfunction statistics in chaotic and weakly disordered quantum systems which goes beyond random matrix theory, supersymmetry techniques, and existing semiclassical methods. The approach is based on a generalization of Berry’s random wave model, combined with a consistent semiclassical representation of spatial two-point correlations. We derive closed expressions for arbitrary wave-function averages in terms of universal coefficients and sums over classical paths, which contain, besides the supersymmetry results, novel oscillatory contributions. Their physical relevance is demonstrated in the context of Coulomb blockade physics.

Figure 1

Normalized Coulomb blockade conductance peak height distribution $P(g)/P^{\mathrm{RMT}}(g)$ for a disordered quantum dot [Eq. (19)]. Deviations from universality (squares) are depicted for values 0.12 (plus symbol), 0.06 (times symbol), and 0.03 (asterisk symbol) of the small parameter $(1/\pi g_0)\ln (L/l)$.