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

@article{Berry2011SlowNC, 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}, year={2011}, volume={44} }

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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