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Slow non-Hermitian cycling: exact solutions and the Stokes phenomenon

Research output: Contribution to journalArticle

Original languageEnglish
Article number435303
Number of pages26
JournalJournal of Physics A: Mathematical and Theoretical
Volume44
Issue number43
DOIs
DatePublished - 28 Oct 2011

Abstract

For non-Hermitian Hamiltonians with an isolated degeneracy ('exceptional point'), a model for cycling around loops that enclose or exclude the degeneracy is solved exactly in terms of Bessel functions. Floquet solutions, returning exactly to their initial states (up to a constant) are found, as well as exact expressions for the adiabatic multipliers when the evolving states are represented as a superposition of eigenstates of the instantaneous Hamiltonian. Adiabatically (i.e. for slow cycles), the multipliers of exponentially subdominant eigenstates can vary wildly, unlike those driven by Hermitian operators, which change little. These variations are explained as an example of the Stokes phenomenon of asymptotics. Improved (superadiabatic) approximations tame the variations of the multipliers but do not eliminate them.

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