Quantitative Conditions Do Not Guarantee the Validity of the Adiabatic Approximation
- 9 September 2005
- journal article
- editorial
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 95 (11), 110407
- https://doi.org/10.1103/PhysRevLett.95.110407
Abstract
In this Letter, we point out that the widely used quantitative conditions in the adiabatic theorem are insufficient in that they do not guarantee the validity of the adiabatic approximation. We also reexamine the inconsistency issue raised by Marzlin and Sanders [Phys. Rev. Lett. 93, 160408 (2004)] and elucidate the underlying cause. DOI: http://dx.doi.org/10.1103/PhysRevLett.95.110407 © 2005 The American Physical SocietyKeywords
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This publication has 17 references indexed in Scilit:
- A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete ProblemScience, 2001
- Adiabatic Theorem without a Gap ConditionCommunications in Mathematical Physics, 1999
- Quantum adiabatic approximation, quantum action, and Berry's phasePhysics Letters A, 1997
- Quantal phase factors accompanying adiabatic changesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1984
- Bound States in Quantum Field TheoryPhysical Review B, 1951
- On the Adiabatic Theorem of Quantum MechanicsJournal of the Physics Society Japan, 1950
- On Nonadiabatic Processes in Inhomogeneous FieldsPhysical Review B, 1937
- Non-adiabatic crossing of energy levelsProceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1932
- Beweis des AdiabatensatzesThe European Physical Journal A, 1928
- Adiabatische Invarianten und QuantentheorieAnnalen der Physik, 1916