Cornell University

Title: Wavefunctions in the crossover between random matrix ensembles

Abstract: Random matrix theory predicts the statistical distribution of energy levels and wavefunctions in disordered metal grains and quantum dots. The probability distributions depend on the fundamental symmetries of the ensemble: presence or absence of time-reversal symmetry and spin-rotation symmetry. Depending on the symmetry class, wavefunction elements are random Gaussian real, complex, or quaternion numbers. In random-matrix ensembles that interpolate between the basic ensembles, distributions are non-Gaussian and there exist correlations between elements of the same wavefunction and between different wavefunctions. We discuss three consequences of such correlations: (1) Enhanced fluctuations of the electron-electron interaction matrix elements, (2) Correlations between Coulomb blockade peak heights at weak magnetic fields, and (3) fluctuations of g-factors and interaction effects in small metal grains.