Chaotic quantum dots with strongly correlated electrons

Abstract

Quantum dots pose a problem where one must confront three obstacles: randomness, interactions and finite size. Yet it is this confluence that allows one to make some theoretical advances by invoking three theoretical tools: Random Matrix theory (RMT), the Renormalization Group (RG) and the 1/N expansion. Here the reader is introduced to these techniques and shown how they may be combined to answer a set of questions pertaining to quantum dots

latex file 16 pages 8 figures, to appear in Reviews of Modern Physics

References in corpus (14)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Renormalization Group Approach to Interacting Fermions
• Statistics of energy levels and eigenfunctions in disordered systems
• The Statistical Theory of Quantum Dots
• Quantum Effects in Coulomb Blockade
• Quantum Theory of a Nematic Fermi Fluid
• Interactions and Interference in Quantum Dots: Kinks in Coulomb Blockade Peak Positions
• Mesoscopic fluctuations of the ground state spin of a small metal particle
• Interactions and Disorder in Quantum Dots: Instabilities and Phase Transitions
• Quantum Dots with Disorder and Interactions: A Solvable Large-g Limit
• A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade
• On the scaling approach to electron-electron interactions in a chaotic quantum dot
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• Ballistic Quantum Dots with Disorder and Interactions: A numerical study on the Robnik-Berry billiard

Cited by in corpus (3)

• Electron energy level statistics in graphene quantum dots
• Development of effective stochastic potential method using random matrix theory for efficient conformational sampling of semiconductor nanoparticles at non-zero temperatures
• Statistical analysis of the figure of merit of a two-level thermoelectric system: a random matrix approach