Statistical Analysis of Magnetic Field Spectra

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 is a new problem which 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 Gaussian Unitary Ensemble, while the higher part obeys a Poissonlike behavior. We also found that the “B-spectrum” fluctuations of the chaotic system are consistent with the results we obtained from random matrices.