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

  title={Slow non-Hermitian cycling: exact solutions and the Stokes phenomenon},
  author={M V Berry and Raam Uzdin},
  journal={Journal of Physics A: Mathematical and Theoretical},
  • M. Berry, R. Uzdin
  • Published 28 October 2011
  • Physics
  • Journal of Physics A: Mathematical and Theoretical
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… 
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