Diagrammatic method of integration over the unitary group, with applications to quantum transport in mesoscopic systems

Abstract

A diagrammatic method is presented for averaging over the circular ensemble of random-matrix theory. The method is applied to phase-coherent conduction through a chaotic cavity (a ``quantum dot'') and through the interface between a normal metal and a superconductor.

arXiv comment37 pages RevTeX, 21 postscript figures included

References in corpus (12)

• Mesoscopic Transport Through Ballistic Cavities: A Random S-Matrix Theory Approach
• Universal Quantum Signatures of Chaos in Ballistic Transport
• GENERALIZED CIRCULAR ENSEMBLE OF SCATTERING MATRICES FOR A CHAOTIC CAVITY WITH NON-IDEAL LEADS
• Random Matrix Theory of a Chaotic Andreev Quantum Dot
• How Phase-Breaking Affects Quantum Transport Through Chaotic Cavities
• Exact Solution for the Distribution of Transmission Eigenvalues in a Disordered Wire and Comparison with Random-Matrix Theory
• Correlation Functions in Disordered Systems
• Effect of a Voltage Probe on the Phase-Coherent Conductance of a Ballistic Chaotic Cavity
• Conductance Distribution of a Quantum Dot with Non-Ideal Single-Channel Leads
• Weak Localization Coexisting with a Magnetic Field in a Normal-Metal--Superconductor Microbridge
• Insensitivity to Time-Reversal Symmetry Breaking of Universal Conductance Fluctuations with Andreev Reflection
• Universality of Weak Localization in Disordered Wires

Cited by in corpus (181)

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• The Role of Spin-Dependent Interface Scattering in Generating Current-Induced Torques in Magnetic Multilayers
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• Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states
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