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Geometry of an adiabatic passage at a level crossing

Mateusz Cholascinski
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Abstract

We discuss adiabatic quantum phenomena at a level crossing. Given a path in the parameter space which passes through a degeneracy point, we find a criterion which determines whether the adiabaticity condition can be satisfied. For paths that can be traversed adiabatically we also derive a differential equation which specifies the time dependence of the system parameters, for which transitions between distinct energy levels can be neglected. We also generalize the well-known geometric connections to the case of adiabatic paths containing arbitrarily many level-crossing points and degenerate levels.

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Mateusz Cholascinski. 2005-06-23. Geometry of an adiabatic passage at a level crossing. https://doi.org/10.1103/physreva.71.063409

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