# Random matrix model for quantum dots and the conductance peak spacing distribution

## Abstract

We introduce a random interaction matrix model (RIMM) for finite-size strongly interacting fermionic systems whose single-particle dynamics is chaotic. The model is applied to Coulomb blockade quantum dots with irregular shape to describe the crossover of the peak spacing distribution from a Wigner-Dyson to a Gaussian-like distribution. The crossover is universal within the random matrix model and is shown to depend on a single parameter: a scaled fluctuation width of the interaction matrix elements. The crossover observed in the RIMM is compared with the results of an Anderson model with Coulomb interactions. (c) 2000 The American Physical Society.

- Authors:

- Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520 (United States)

- Publication Date:

- OSTI Identifier:
- 20216569

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. B, Condensed Matter and Materials Physics

- Additional Journal Information:
- Journal Volume: 61; Journal Issue: 20; Other Information: PBD: 15 May 2000; Journal ID: ISSN 1098-0121

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE; SEMICONDUCTOR JUNCTIONS; FERMIONS; TRANSPORT THEORY; RANDOMNESS; THEORETICAL DATA

### Citation Formats

```
Alhassid, Y., Jacquod, Ph., and Wobst, A.
```*Random matrix model for quantum dots and the conductance peak spacing distribution*. United States: N. p., 2000.
Web. doi:10.1103/PhysRevB.61.R13357.

```
Alhassid, Y., Jacquod, Ph., & Wobst, A.
```*Random matrix model for quantum dots and the conductance peak spacing distribution*. United States. doi:10.1103/PhysRevB.61.R13357.

```
Alhassid, Y., Jacquod, Ph., and Wobst, A. Mon .
"Random matrix model for quantum dots and the conductance peak spacing distribution". United States. doi:10.1103/PhysRevB.61.R13357.
```

```
@article{osti_20216569,
```

title = {Random matrix model for quantum dots and the conductance peak spacing distribution},

author = {Alhassid, Y. and Jacquod, Ph. and Wobst, A.},

abstractNote = {We introduce a random interaction matrix model (RIMM) for finite-size strongly interacting fermionic systems whose single-particle dynamics is chaotic. The model is applied to Coulomb blockade quantum dots with irregular shape to describe the crossover of the peak spacing distribution from a Wigner-Dyson to a Gaussian-like distribution. The crossover is universal within the random matrix model and is shown to depend on a single parameter: a scaled fluctuation width of the interaction matrix elements. The crossover observed in the RIMM is compared with the results of an Anderson model with Coulomb interactions. (c) 2000 The American Physical Society.},

doi = {10.1103/PhysRevB.61.R13357},

journal = {Physical Review. B, Condensed Matter and Materials Physics},

issn = {1098-0121},

number = 20,

volume = 61,

place = {United States},

year = {2000},

month = {5}

}

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