# Quantum and spectral properties of the Labyrinth model

## Abstract

We consider the Labyrinth model, which is a two-dimensional quasicrystal model. We show that the spectrum of this model, which is known to be a product of two Cantor sets, is an interval for small values of the coupling constant. We also consider the density of states measure of the Labyrinth model and show that it is absolutely continuous with respect to Lebesgue measure for almost all values of coupling constants in the small coupling regime.

- Authors:

- Department of Mathematics, University of California, Irvine, California 92697 (United States)

- Publication Date:

- OSTI Identifier:
- 22596855

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 6; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COUPLING CONSTANTS; DENSITY OF STATES; QUANTUM SYSTEMS; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Takahashi, Yuki, E-mail: takahasy@math.uci.edu.
```*Quantum and spectral properties of the Labyrinth model*. United States: N. p., 2016.
Web. doi:10.1063/1.4953379.

```
Takahashi, Yuki, E-mail: takahasy@math.uci.edu.
```*Quantum and spectral properties of the Labyrinth model*. United States. doi:10.1063/1.4953379.

```
Takahashi, Yuki, E-mail: takahasy@math.uci.edu. Wed .
"Quantum and spectral properties of the Labyrinth model". United States.
doi:10.1063/1.4953379.
```

```
@article{osti_22596855,
```

title = {Quantum and spectral properties of the Labyrinth model},

author = {Takahashi, Yuki, E-mail: takahasy@math.uci.edu},

abstractNote = {We consider the Labyrinth model, which is a two-dimensional quasicrystal model. We show that the spectrum of this model, which is known to be a product of two Cantor sets, is an interval for small values of the coupling constant. We also consider the density of states measure of the Labyrinth model and show that it is absolutely continuous with respect to Lebesgue measure for almost all values of coupling constants in the small coupling regime.},

doi = {10.1063/1.4953379},

journal = {Journal of Mathematical Physics},

number = 6,

volume = 57,

place = {United States},

year = {Wed Jun 15 00:00:00 EDT 2016},

month = {Wed Jun 15 00:00:00 EDT 2016}

}

DOI: 10.1063/1.4953379

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