General conditions for quantum adiabatic evolution

Journal Article · Wed Jul 15 04:00:00 EDT 2009 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.80.012106· OSTI ID:21313200

Comparat, Daniel ^[1]

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1. Laboratoire Aime Cotton, CNRS, Universite Paris-Sud, Batiment 505, 91405 Orsay (France)

Adiabaticity occurs when, during its evolution, a physical system remains in the instantaneous eigenstate of the Hamiltonian. Unfortunately, existing results, such as the quantum adiabatic theorem based on a slow down evolution [H({epsilon}t),{epsilon}{yields}0], are insufficient to describe an evolution driven by the Hamiltonian H(t) itself. Here we derive general criteria and exact bounds, for the state and its phase, ensuring an adiabatic evolution for any Hamiltonian H(t). As a corollary, we demonstrate that the commonly used condition of a slow Hamiltonian variation rate, compared to the spectral gap, is indeed sufficient to ensure adiabaticity but only when the Hamiltonian is real and nonoscillating (for instance, containing exponential or polynomial but no sinusoidal functions)

• OSTI ID: 21313200
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 80; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENFUNCTIONS
EIGENVALUES
EVOLUTION
HAMILTONIANS
POLYNOMIALS
VARIATIONS