Generalization of Berry’s geometric phase, equivalence of the Hamiltonian nature, quantizability and strong stability of linear oscillatory systems, and conservation of adiabatic invariants

DOI10.1063/1.1506954zbMath1060.81030OpenAlexW2109007256MaRDI QIDQ4832813

Konstantin Y. Bliokh

Publication date: 14 December 2004

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.1506954

Mathematics Subject Classification ID

Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Stability of manifolds of solutions to ordinary differential equations (34D35)

Cites Work

• Remarks on eigenvalues and eigenvectors of Hermitian matrices, Berry phase, adiabatic connections and quantum Hall effect
• Adiabatic invariants for linear Hamiltonian systems
• Geometric amplitude, adiabatic invariants, quantization, and strong stability of Hamiltonian systems

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