Hannay angles and Grassmannian action-angle quantum states

DOI10.1134/S0040577920020075zbMath1445.81028OpenAlexW3012628307MaRDI QIDQ2193684

H. Lakehal, Mustapha Maamache

Publication date: 20 August 2020

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0040577920020075

zbMATH Keywords

Berry phaseHannay angleaction-angle fermionic coherent state

Mathematics Subject Classification ID

Coherent states (81R30) Hamilton-Jacobi equations in mechanics (70H20) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Canonical transformations in symplectic and contact geometry (53D22) Fermionic systems in quantum theory (81V74)

Cites Work

• The connection whose holonomy is the classical adiabatic angles of Hannay and Berry and its generalization to the non-integrable case
• The Hannay angles: Geometry, adiabaticity, and an example
• Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic section
• Fermionic coherent states
• Nonlinear fermions and coherent states
• Berry's phase, Hannay's angle and coherent states
• Fermionic coherent states for pseudo-Hermitian two-level systems
• Generalized Grassmannian coherent states for pseudo-Hermitiann-level systems
• Quantal phase factors accompanying adiabatic changes
• Classical adiabatic angles and quantal adiabatic phase
• Berry's phase and Hannay's angle from quantum canonical transformations

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