Noncommutative algebras, nano-structures, and quantum dynamics generated by resonances. III.

DOI10.1134/S1061920806020026zbMath1129.46064WikidataQ125634762 ScholiaQ125634762MaRDI QIDQ871764

Mikhail V. Karasev

Publication date: 26 March 2007

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

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05) Geometry and quantization, symplectic methods (81S10) Noncommutative geometry in quantum theory (81R60) Applications of functional analysis in quantum physics (46N50)

Related Items (9)

Minimal basis of the symmetry algebra for three-frequency resonance ⋮ Magneto-metric Hamiltonians on quantum surfaces in the configuration space ⋮ Bi-states and 2-level systems in rectangular Penning traps ⋮ Instantons via breaking geometric symmetry in hyperbolic traps ⋮ Normal form of a quantum Hamiltonian with one and a half degrees of freedom near a hyperbolic fixed point ⋮ Asymptotics of the spectrum and quantum averages of a perturbed resonant oscillator near the boundaries of spectral clusters ⋮ Geometric dynamics on quantum nano-surfaces and low-energy spectrum in a homogeneous magnetic field ⋮ Asymptotics of the spectrum of the hydrogen atom in a magnetic field near the lower boundaries of spectral clusters ⋮ Inserted perturbations generating asymptotical integrability

Cites Work

• New global asymptotics and anomalies for the problem of quantization of the adiabatic invariant
• Quasi-modes sur les variétés Riemanniennes
• On the construction of quasimodes associated with stable periodic orbits
• Asymptotics of eigenvalue clusters for the Laplacian plus a potential
• Integrals over membranes, transition amplitudes, and quantization
• Quantization and coherent states over Lagrangian submanifolds
• Formulas for noncommutative products of functions in terms of membranes and strings. I
• Representation of the evolution operator via membrane amplitudes
• Quantization of Kähler manifolds. I: Geometric interpretation of Berezin's quantization
• Non-Lie permutation relations
• Eigenvalues associated with a closed geodesic
• Quantum surfaces, special functions, and the tunneling effect
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