Geometric phase around exceptional points

Details Geometric phase around exceptional points Geometric phase around exceptional points

2005-01-10

arxiv.org/abs/quant-ph/0501040v4

Phys. Rev A 72, 014104 (2005)

Physics

Quantum Physics

4 pages, 1 figure, with revisions in the introduction and conclusion

Scientific paper

10.1103/PhysRevA.72.014104

A wave function picks up, in addition to the dynamic phase, the geometric (Berry) phase when traversing adiabatically a closed cycle in parameter space. We develop a general multidimensional theory of the geometric phase for (double) cycles around exceptional degeneracies in non-Hermitian Hamiltonians. We show that the geometric phase is exactly $\pi$ for symmetric complex Hamiltonians of arbitrary dimension and for nonsymmetric non-Hermitian Hamiltonians of dimension 2. For nonsymmetric non-Hermitian Hamiltonians of higher dimension, the geometric phase tends to $\pi$ for small cycles and changes as the cycle size and shape are varied. We find explicitly the leading asymptotic term of this dependence, and describe it in terms of interaction of different energy levels.

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