Statistical analysis of magnetic-field spectra

Abstract

We have calculated and statistically analyzed the magnetic-field spectrum (the B spectrum) at fixed electron Fermi energy for two quantum dot systems with classically chaotic shape. This problem arises naturally in transport measurements where the incoming electron has a fixed energy while one tunes the magnetic field to obtain resonance conductance patterns. The B spectrum, defined as the collection of values {Bi} at which conductance g(Bi) takes extremal values, is determined by a quadratic eigenvalue equation, in distinct difference to the usual linear eigenvalue problem satisfied by the energy levels. We found that the lower part of the B spectrum satisfies the distribution belonging to the Gaussian unitary ensemble, while the higher part obeys a Poisson-like behavior. We also found that the B spectrum fluctuations of the chaotic system are consistent with the results we obtained from random matrices.