The Quantum Adiabatic Approximation and the Geometric Phase

Abstract

A precise definition of an adiabaticity parameter ν of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator U(τ) = ∑ l U (l)(τ) with U (l)(τ) being at least of the order ν. In particular U (0)(τ) corresponds to the adiabatic approximation and… (More)

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