A Unified View on Geometric Phases and Exceptional Points in Adiabatic Quantum Mechanics

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2022
• Hauptverfasser: Pap, Eric J., Boer, Daniël, Waalkens, Holger
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2022
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/211542
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: A Unified View on Geometric Phases and Exceptional Points in Adiabatic Quantum Mechanics. Eric J. Pap, Daniël Boer and Holger Waalkens. SIGMA 18 (2022), 003, 42 pages

We present a formal geometric framework for the study of adiabatic quantum mechanics for arbitrary finite-dimensional non-degenerate Hamiltonians. This framework generalizes earlier holonomy interpretations of the geometric phase to non-cyclic states appearing for non-Hermitian Hamiltonians. We star...