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Statistics of wave functions in disordered systems with applications to Coulomb blockade peak spacing

Publication ,  Journal Article
Miller, M; Ullmo, D; Baranger, HU
Published in: Physical Review B - Condensed Matter and Materials Physics
July 15, 2005

Despite considerable work on the energy-level and wave function 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 wave function. 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. © 2005 The American Physical Society.

Duke Scholars

Published In

Physical Review B - Condensed Matter and Materials Physics

DOI

EISSN

1550-235X

ISSN

1098-0121

Publication Date

July 15, 2005

Volume

72

Issue

4

Related Subject Headings

  • Fluids & Plasmas
  • 09 Engineering
  • 03 Chemical Sciences
  • 02 Physical Sciences
 

Citation

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Miller, M., Ullmo, D., & Baranger, H. U. (2005). Statistics of wave functions in disordered systems with applications to Coulomb blockade peak spacing. Physical Review B - Condensed Matter and Materials Physics, 72(4). https://doi.org/10.1103/PhysRevB.72.045305
Miller, M., D. Ullmo, and H. U. Baranger. “Statistics of wave functions in disordered systems with applications to Coulomb blockade peak spacing.” Physical Review B - Condensed Matter and Materials Physics 72, no. 4 (July 15, 2005). https://doi.org/10.1103/PhysRevB.72.045305.
Miller M, Ullmo D, Baranger HU. Statistics of wave functions in disordered systems with applications to Coulomb blockade peak spacing. Physical Review B - Condensed Matter and Materials Physics. 2005 Jul 15;72(4).
Miller, M., et al. “Statistics of wave functions in disordered systems with applications to Coulomb blockade peak spacing.” Physical Review B - Condensed Matter and Materials Physics, vol. 72, no. 4, July 2005. Scopus, doi:10.1103/PhysRevB.72.045305.
Miller M, Ullmo D, Baranger HU. Statistics of wave functions in disordered systems with applications to Coulomb blockade peak spacing. Physical Review B - Condensed Matter and Materials Physics. 2005 Jul 15;72(4).

Published In

Physical Review B - Condensed Matter and Materials Physics

DOI

EISSN

1550-235X

ISSN

1098-0121

Publication Date

July 15, 2005

Volume

72

Issue

4

Related Subject Headings

  • Fluids & Plasmas
  • 09 Engineering
  • 03 Chemical Sciences
  • 02 Physical Sciences