Universal Correlations of Coulomb Blockade Conductance Peaks and the Rotation Scaling in Quantum Dots

Abstract

We show that the parametric correlations of the conductance peak amplitudes of a chaotic or weakly disordered quantum dot in the Coulomb blockade regime become universal upon an appropriate scaling of the parameter. We compute the universal forms of this correlator for both cases of conserved and broken time reversal symmetry. For a symmetric dot the correlator is independent of the details in each lead such as the number of channels and their correlation. We derive a new scaling, which we call the rotation scaling, that can be computed directly from the dot's eigenfunction rotation rate or alternatively from the conductance peak heights, and therefore does not require knowledge of the spectrum of the dot. The relation of the rotation scaling to the level velocity scaling is discussed. The exact analytic form of the conductance peak correlator is derived at short distances. We also calculate the universal distributions of the average level width velocity for various values of the scaled parameter. The universality is illustrated in an Anderson model of a disordered dot.

35 pages, RevTex, 6 Postscript figures

References in corpus (4)

• Quantum chaos in a deformable billiard: Applications to quantum dots
• Universal Parametric Correlations of Conductance Peaks in Quantum Dots
• Statistical Properties of Level Widths and Conductance Peaks in a Quantum Dot
• Universal Parametric Correlations of Eigenfunctions in Chaotic and Disordered Systems

Cited by in corpus (6)

• The Statistical Theory of Quantum Dots
• Quantum Effects in Coulomb Blockade
• Statistics of resonance width shifts as a signature of eigenfunction non-orthogonality
• Quantum Chaos in Open versus Closed Quantum Dots: Signatures of Interacting Particles
• Orthogonality Catastrophe in Parametric Random Matrices
• Weak Localization in the Conductance Peaks of Coulomb Blockade Quantum Dots