Superparabolic Level Glancing Models for Two-State Quantum Systems
arXiv:1205.6604 · doi:10.1103/PhysRevA.86.033415
Abstract
Level crossing models for two-state quantum systems are applicable to a wide variety of physical problems. We address the special case of level glancing, i.e., when energy levels reach a degeneracy at a specific point of time, but never actually cross. The simplest model with such behaviour is the parabolic model, and its generalizations, which we call superparabolic models. We discuss their basic characteristics, complementing the previous work on the related nonlinear crossing models [Phys. Rev. A 59, 4580 (1999)].
11 pages, 7 figures
References in corpus (5)
- Non-adiabatic Level Crossing in Resonant Neutrino Oscillations
- Optimal non-linear passage through a quantum critical point
- Variational ansatz for the nonlinear Landau-Zener problem for cold atom association
- Dynamics of periodic anticrossings: Decoherence, pointer states and hysteresis curves
- Landau-Zener problem in a three-level neutrino system with non-linear time dependence
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