Phys. Rev. Lett. 93, 160408 (2004) [4 pages]Inconsistency in the Application of the Adiabatic TheoremReceived 4 April 2004; published 15 October 2004 The adiabatic theorem states that an initial eigenstate of a slowly varying Hamiltonian remains close to an instantaneous eigenstate of the Hamiltonian at a later time. We show that a perfunctory application of this statement is problematic if the change in eigenstate is significant, regardless of how closely the evolution satisfies the requirements of the adiabatic theorem. We also introduce an example of a two-level system with an exactly solvable evolution to demonstrate the inapplicability of the adiabatic approximation for a particular slowly varying Hamiltonian. © 2004 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.93.160408
DOI:
10.1103/PhysRevLett.93.160408
PACS:
03.65.Ca, 03.65.Ta
See AlsoComment: Jie Ma, Yongping Zhang, Enge Wang, and Biao Wu, Comment II on “Inconsistency in the Application of the Adiabatic Theorem”, Phys. Rev. Lett. 97, 128902 (2006). Comment: Solomon Duki, H. Mathur, and Onuttom Narayan, Comment I on “Inconsistency in the Application of the Adiabatic Theorem”, Phys. Rev. Lett. 97, 128901 (2006). Reply: Karl-Peter Marzlin and Barry C. Sanders, Marzlin and Sanders Reply:, Phys. Rev. Lett. 97, 128903 (2006). |
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