Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-10-25
Commun.Math.Phys. 218 (2001) 233-244
Physics
High Energy Physics
High Energy Physics - Theory
14 pages, 2 ps-figures, to appear in Commun. Math. Phys
Scientific paper
10.1007/s002200100390
We show that nodal points of ground states of some quantum systems with magnetic interactions can be identified in simple geometric terms. We analyse in detail two different archetypical systems: i) a planar rotor with a non-trivial magnetic flux $\Phi$, ii) Hall effect on a torus. In the case of the planar rotor we show that the level repulsion generated by any reflection invariant potential $V$ is encoded in the nodal structure of the unique vacuum for $\theta=\pi$. In the second case we prove that the nodes of the first Landau level for unit magnetic charge appear at the crossing of the two non-contractible circles $\alpha_-$, $\beta_-$ with holonomies $h_{\alpha_-}(A)= h_{\beta_-}(A)=-1$ for any reflection invariant potential $V$. This property illustrates the geometric origin of the quantum translation anomaly.
Aguado Miguel
Asorey Manuel
Esteve José G.
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