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 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 $B_i$ at which conductance $g(B_i)$ 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 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.

References in corpus (4)

• Quantum Transport in Semiconductor Nanostructures
• Gate-Voltage Studies of Discrete Electronic States in Al Nanoparticles
• Fractal Conductance Fluctuations in a Soft Wall Stadium and a Sinai Billiard
• Parametric Correlations of Phase Shifts and Statistics of Time Delays in Quantum Chaotic Scattering: Crossover between Unitary and Orthogonal Symmetries