Analytical Results for the Dynamics of Parabolic Level-Crossing Model

Abstract

We study the dynamics of a two-level crossing model with a parabolic separation of the diabatic energies. The solutions are expressed in terms of the tri-confluent Heun equations --- the generalization of the confluent hypergeometric equations. We obtain analytical approximations for the state populations in terms of Airy and Bessel functions. Applicable expressions are derived for a large part of the parameter space. We also provide simple formulas which connect local solution in different time regimes. The validity of the analytical approximations is shown by comparing them to numerical simulations.

arXiv comment11 pages, 4 figures

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Cited by in corpus (4)

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• Non-adiabatic transitions in parabolic and super-parabolic $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian systems
• Efficient electron transfer in quantum dot chains controlled by a cubic detuning profile via shortcuts to adiabaticity