Bounds for nonadiabatic transitions

Abstract

We discuss bounds for nonadiabatic transitions from the viewpoints of the adiabatic perturbation theory and the quantum speed limit. We show that the amount of nonadiabatic transitions from the $n$th level to the $m$th level is bounded by a function of the quantum geometric tensor for the $m$th level. We analyze this bound from the viewpoint of the adiabatic perturbation theory. In addition, this bound and the viewpoint of the quantum speed limit suggest nontrivial relationship between the dynamical transformation and the adiabatic transformation. We also derive a universal bound for any nonadiabatic transition. This bound is written in terms of the counterdiabatic Hamiltonian.

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• Universal adiabatic dynamics across a quantum critical point
• Bounds for the adiabatic approximation with applications to quantum computation
• Quantum Adiabatic Brachistochrone
• Universal Work Fluctuations during Shortcuts To Adiabaticity by Counterdiabatic Driving
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
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Cited by in corpus (1)

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