Geometric phase around exceptional points
By Alexei A. Mailybaev, Oleg N. Kirillov, A. P. Seyranian. Physical Review A, 2005
145 citations recorded by the source corpus.
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.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/b4ba68c52568c724d48016a5f3bf613b75037982
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In Atomic and Molecular Physics, and Optics
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In Statistical and Nonlinear Physics
Citations in the corpus
- Geometric phase from Aharonov–Bohm to Pancharatnam–Berry and beyond (2019, background): “etween ||n and , correspond to non-adiabatic corrections. The eTn1|| term is a non-universal constant. Interestingly, the geometric phase can have a topological character in non-Hermitian systems (82,83,84). 2. Mathematical formalism The distinguishing feature of geometric phases is that, unlike dyn”
- Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems. (2016, background): “Previous researchers [11, 12, 16, 38] have focused on the winding numbers of the eigenvectors ψ±.”
- Biorthogonal quantum mechanics (2013, background): “The results of [17] reproduced here for the first-order perturbation expansion lends itself naturally with the analysis of geometric phases for complex Hamiltonians [31, 32, 33, 34].”