Statistics of Wave Functions in Disordered Systems with Applications to Coulomb Blockade Peak Spacing
arXiv:cond-mat/0406493 · doi:10.1103/PhysRevB.72.045305
Abstract
Despite considerable work on the energy-level and wavefunction statistics of disordered quantum systems, numerical studies of those statistics relevant for electron-electron interactions in mesoscopic systems have been lacking. We plug this gap by using a tight-binding model to study a wide variety of statistics for the two-dimensional, disordered quantum system in the diffusive regime. Our results are in good agreement with random matrix theory (or its extensions) for simple statistics such as the probability distribution of energy levels or spatial correlation of a wavefunction. However, we see substantial disagreement in several statistics which involve both integrating over space and different energy levels, indicating that disordered systems are more complex than previously thought. These are exactly the quantities relevant to electron-electron interaction effects in quantum dots; in fact, we apply these results to the Coulomb blockade, where we find altered spacings between conductance peaks and wider spin distributions than traditionally expected.
arXiv commentAccepted for publication in Phys Rev B
References in corpus (17)
- Random-Matrix Theory of Quantum Transport
- Random Matrix Theories in Quantum Physics: Common Concepts
- Statistics of energy levels and eigenfunctions in disordered systems
- Quantum Effects in Coulomb Blockade
- Spectroscopy of discrete energy levels in ultrasmall metallic grains
- Fluctuations of the inverse participation ratio at the Anderson transition
- Multifractality and critical fluctuations at the Anderson transition
- Shell filling in closed single-wall carbon nanotube quantum dots
- Experimental studies of Chaos and Localization in Quantum Wavefunctions
- Mesoscopic Fluctuations of Eigenfunctions and "Level Velocity" Distribution in Disordered Metals
- Inelastic Electron Lifetime in Disordered Mesoscopic Systems
- Correlations due to localization in quantum eigenfunctions of disordered microwave cavities
- Long-Range Spatial Correlations of Eigenfunctions in Quantum Disordered Systems
- Comment on "Spatial Correlation in Quantum Chaotic Systems with Time-Reversal Symmetry: Theory and Experiment" by V. N. Prigodin et al [cond-mat/9504089]
- Interactions in Chaotic Nanoparticles: Fluctuations in Coulomb Blockade Peak Spacings
- Chaos and Interacting Electrons in Ballistic Quantum Dots
- Spin and e-e interactions in quantum dots: Leading order corrections to universality and temperature effects