Validity of the Adiabatic Approximation

Abstract

We analyze the validity of the adiabatic approximation, and in particular the reliability of what has been called the "standard criterion" for validity of this approximation. Recently, this criterion has been found to be insufficient. We will argue that the criterion is sufficient only when it agrees with the intuitive notion of slowness of evolution of the Hamiltonian. However, it can be insufficient in cases where the Hamiltonian varies rapidly but only by a small amount. We also emphasize the distinction between the adiabatic {\em theorem} and the adiabatic {\em approximation}, two quite different although closely related ideas.

4 pages, 1 figure

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• Beyond the Quantum Adiabatic Approximation: Adiabatic Perturbation Theory
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• Improved Error Bounds for the Adiabatic Approximation
• Exploring adiabatic quantum trajectories via optimal control
• Adiabatic Condition and Quantum Geometric Potential
• Quantum adiabatic theorem in light of the Marzlin-Sanders inconsistency
• The adiabatic theorem in the presence of noise
• Why the Quantitative Condition Fails to Reveal Quantum Adiabaticity
• Quantum adiabatic evolution with energy-degeneracy levels
• Optimizing adiabaticity in quantum mechanics
• Born-Oppenheimer approximation in open systems
• Avoid First Order Quantum Phase Transition by Changing Problem Hamiltonians
• A numerical approach for calculating exact non-adiabatic terms in quantum dynamics
• Hierarchical Theory of Quantum Adiabatic Evolution
• Matrix Operator Approach to the Quantum Evolution Operator and the Geometric Phase
• Femtosecond pulses and dynamics of molecular photoexcitation: RbCs example
• Born-Oppenheimer approximation for open quantum systems within the quantum trajectory approach
• General conditions for a quantum adiabatic evolution
• Geometric Floquet Condition for Quantum Adiabaticity