### Abstract

Parametrized families of Landau Hamiltonians are introduced, where the parameter space is the Teichmüller space (topologically the complex upper half plane) corresponding to deformations of tori. The underlying SO(2,1) symmetry of the families enables an explicit calculation of the Berry phases picked up by the eigenstates when the torus is slowly deformed. It is also shown that apart from these phases that are local in origin, there are global non-Abelian ones too, related to the hidden discrete symmetry group Γ_{θ} (the theta group, which is a subgroup of the modular group) of the families. The induced Riemannian structure on the parameter space is the usual Poincare metric on the upper half plane of constant negative curvature. Due to the discrete symmetry Γ_{θ} the geodesic motion restricted to the fundamental domain of this group is chaotic.

Original language | English |
---|---|

Pages (from-to) | 2792-2802 |

Number of pages | 11 |

Journal | Journal of Mathematical Physics |

Volume | 36 |

Issue number | 6 |

Publication status | Published - 1995 |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

*Journal of Mathematical Physics*,

*36*(6), 2792-2802.

**Berry phases for Landau Hamiltonians on deformed tori.** / Lévay, P.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 36, no. 6, pp. 2792-2802.

}

TY - JOUR

T1 - Berry phases for Landau Hamiltonians on deformed tori

AU - Lévay, P.

PY - 1995

Y1 - 1995

N2 - Parametrized families of Landau Hamiltonians are introduced, where the parameter space is the Teichmüller space (topologically the complex upper half plane) corresponding to deformations of tori. The underlying SO(2,1) symmetry of the families enables an explicit calculation of the Berry phases picked up by the eigenstates when the torus is slowly deformed. It is also shown that apart from these phases that are local in origin, there are global non-Abelian ones too, related to the hidden discrete symmetry group Γθ (the theta group, which is a subgroup of the modular group) of the families. The induced Riemannian structure on the parameter space is the usual Poincare metric on the upper half plane of constant negative curvature. Due to the discrete symmetry Γθ the geodesic motion restricted to the fundamental domain of this group is chaotic.

AB - Parametrized families of Landau Hamiltonians are introduced, where the parameter space is the Teichmüller space (topologically the complex upper half plane) corresponding to deformations of tori. The underlying SO(2,1) symmetry of the families enables an explicit calculation of the Berry phases picked up by the eigenstates when the torus is slowly deformed. It is also shown that apart from these phases that are local in origin, there are global non-Abelian ones too, related to the hidden discrete symmetry group Γθ (the theta group, which is a subgroup of the modular group) of the families. The induced Riemannian structure on the parameter space is the usual Poincare metric on the upper half plane of constant negative curvature. Due to the discrete symmetry Γθ the geodesic motion restricted to the fundamental domain of this group is chaotic.

UR - http://www.scopus.com/inward/record.url?scp=21844516198&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21844516198&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:21844516198

VL - 36

SP - 2792

EP - 2802

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 6

ER -