# Quantum Hall effect in a one-dimensional dynamical system

## Abstract

We construct a periodically time-dependent Hamiltonian with a phase transition in the quantum Hall universality class. One spatial dimension can be eliminated by introducing a second incommensurate driving frequency, so that we can study the quantum Hall effect in a one-dimensional (1D) system. This reduction to 1D is very efficient computationally and would make it possible to perform experiments on the 2D quantum Hall effect using cold atoms in a 1D optical lattice.

- Authors:

- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, NL-2300 RA Leiden (Netherlands)
- Institute of Theoretical Physics, University of Warsaw, Hoza 69, PL-00-681 Warsaw (Poland)

- Publication Date:

- OSTI Identifier:
- 21596870

- Resource Type:
- Journal Article

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

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 11; Other Information: DOI: 10.1103/PhysRevB.84.115133; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1098-0121

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HALL EFFECT; HAMILTONIANS; INTERFERENCE; LASER RADIATION; ONE-DIMENSIONAL CALCULATIONS; PERIODICITY; PHASE TRANSFORMATIONS; QUANTUM MECHANICS; REDUCTION; STARK EFFECT; TIME DEPENDENCE; TWO-DIMENSIONAL CALCULATIONS; CHEMICAL REACTIONS; ELECTROMAGNETIC RADIATION; MATHEMATICAL OPERATORS; MECHANICS; QUANTUM OPERATORS; RADIATIONS; VARIATIONS

### Citation Formats

```
Dahlhaus, J. P., Edge, J. M., Beenakker, C. W. J., and Tworzydlo, J.
```*Quantum Hall effect in a one-dimensional dynamical system*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVB.84.115133.

```
Dahlhaus, J. P., Edge, J. M., Beenakker, C. W. J., & Tworzydlo, J.
```*Quantum Hall effect in a one-dimensional dynamical system*. United States. doi:10.1103/PHYSREVB.84.115133.

```
Dahlhaus, J. P., Edge, J. M., Beenakker, C. W. J., and Tworzydlo, J. Thu .
"Quantum Hall effect in a one-dimensional dynamical system". United States. doi:10.1103/PHYSREVB.84.115133.
```

```
@article{osti_21596870,
```

title = {Quantum Hall effect in a one-dimensional dynamical system},

author = {Dahlhaus, J. P. and Edge, J. M. and Beenakker, C. W. J. and Tworzydlo, J.},

abstractNote = {We construct a periodically time-dependent Hamiltonian with a phase transition in the quantum Hall universality class. One spatial dimension can be eliminated by introducing a second incommensurate driving frequency, so that we can study the quantum Hall effect in a one-dimensional (1D) system. This reduction to 1D is very efficient computationally and would make it possible to perform experiments on the 2D quantum Hall effect using cold atoms in a 1D optical lattice.},

doi = {10.1103/PHYSREVB.84.115133},

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

issn = {1098-0121},

number = 11,

volume = 84,

place = {United States},

year = {2011},

month = {9}

}

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