# Quantum chaos in one dimension?

## Abstract

In this work we investigate the inverse of the celebrated Bohigas-Giannoni-Schmit conjecture. Using two inversion methods we compute a one-dimensional potential whose lowest N eigenvalues obey random matrix statistics. Our numerical results indicate that in the asymptotic limit N{yields}{infinity} the solution is nowhere differentiable and most probably nowhere continuous. Thus such a counterexample does not exist.

- Authors:

- Elmeleti Fizika Tanszek, Fizikai Intezet, Budapesti Muszaki es Gazdasagtudomanyi Egyetem, H-1521 Budapest (Hungary)
- (New Zealand)

- Publication Date:

- OSTI Identifier:
- 21611531

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevE.84.016230; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1539-3755

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; ASYMPTOTIC SOLUTIONS; CHAOS THEORY; EIGENVALUES; MATRICES; ONE-DIMENSIONAL CALCULATIONS; POTENTIALS; QUANTUM MECHANICS; RANDOMNESS; STATISTICS; MATHEMATICAL SOLUTIONS; MATHEMATICS; MECHANICS

### Citation Formats

```
Ujfalusi, Laszlo, Varga, Imre, Schumayer, Daniel, and Department of Physics, University of Otago, 730 Cumberland Street, Dunedin 9016.
```*Quantum chaos in one dimension?*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVE.84.016230.

```
Ujfalusi, Laszlo, Varga, Imre, Schumayer, Daniel, & Department of Physics, University of Otago, 730 Cumberland Street, Dunedin 9016.
```*Quantum chaos in one dimension?*. United States. doi:10.1103/PHYSREVE.84.016230.

```
Ujfalusi, Laszlo, Varga, Imre, Schumayer, Daniel, and Department of Physics, University of Otago, 730 Cumberland Street, Dunedin 9016. Fri .
"Quantum chaos in one dimension?". United States. doi:10.1103/PHYSREVE.84.016230.
```

```
@article{osti_21611531,
```

title = {Quantum chaos in one dimension?},

author = {Ujfalusi, Laszlo and Varga, Imre and Schumayer, Daniel and Department of Physics, University of Otago, 730 Cumberland Street, Dunedin 9016},

abstractNote = {In this work we investigate the inverse of the celebrated Bohigas-Giannoni-Schmit conjecture. Using two inversion methods we compute a one-dimensional potential whose lowest N eigenvalues obey random matrix statistics. Our numerical results indicate that in the asymptotic limit N{yields}{infinity} the solution is nowhere differentiable and most probably nowhere continuous. Thus such a counterexample does not exist.},

doi = {10.1103/PHYSREVE.84.016230},

journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)},

issn = {1539-3755},

number = 1,

volume = 84,

place = {United States},

year = {2011},

month = {7}

}

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