On the geometry of slow-fast phase spaces and the semiclassical quantization

DOI10.1134/S1061920821010039zbMath1470.53073OpenAlexW3138623172MaRDI QIDQ829066

N. Mamani-Alegria, Misael Avendaño-Camacho, Yuri M. Vorobiev

Publication date: 5 May 2021

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

Full work available at URL: https://doi.org/10.1134/s1061920821010039

zbMATH Keywords

semiclassical quantizationslow-fast phase space

Mathematics Subject Classification ID

Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Geometric quantization (53D50)

Related Items (1)

On integrable models close to slow-fast Hamiltonian systems

Cites Work

• Contribution to the symplectic structure in the quantization rule due to noncommutativity of adiabatic parameters
• Homological equations for tensor fields and periodic averaging
• The connection whose holonomy is the classical adiabatic angles of Hannay and Berry and its generalization to the non-integrable case
• Connections on Lagrangian submanifolds and some quasiclassical approximation problems
• New global asymptotics and anomalies for the problem of quantization of the adiabatic invariant
• On the change in the adiabatic invariant on crossing a separatrix in systems with two degrees of freedom
• Adiabatic perturbation theory in quantum dynamics
• The Hannay angles: Geometry, adiabaticity, and an example
• Geometric phases in classical and quantum mechanics
• Reduction, symmetry, and phases in mechanics
• Classical non-adiabatic angles
• Geometric phases and the Bohr-Sommerfeld quantization of multicomponent wave fields
• Deformations of Poisson structures on fibered manifolds and adiabatic slow–fast systems
• New integral representations of the Maslov canonical operator in singular charts
• Higher order corrections to adiabatic invariants of generalized slow-fast Hamiltonian systems
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