5 citations · 8 across the 4 of their papers we have counts for
6 papers
Noncommutative Algebras, Nano-Structures, and Quantum Dynamics Generated by Resonances
Mikhail Karasev
We observe ``quantum'' properties of resonance equilibrium points and resonance univariant submanifolds in the phase space. Resonances between Birkhoff or Floquet--Lyapunov frequen…
Intrinsic Dynamics of Manifolds: Quantum Paths, Holonomy, and Trajectory Localization
Mikhail Karasev
We consider an ``integral'' extension of the classical notion of affine connection providing a correspondence between paths in the manifold and diffeomorphisms of the manifold. The…
Intrinsic Dynamics of Symplectic Manifolds: Membrane Representation and Phase Product
Mikhail Karasev
On general symplectic manifolds we describe a correspondence between symplectic transformations and their phase functions. On the quantum level, this is a correspondence between un…
Quantization and Intrinsic Dynamics
M. V. Karasev
A dynamical scheme of quantization of symplectic manifolds is described. It is based on intrinsic Schrödinger and Heisenberg type nonlinear evolutionary equations with multidimensi…
Coherent transforms and irreducible representations corresponding to complex structures on a cylinder and on a torus
M. V. Karasev, E. M. Novikova
We study a class of algebras with non-Lie commutation relations whose symplectic leaves are surfaces of revolution: a cylinder or a torus. Over each of such surfaces we introduce a…
Quantum surfaces, special functions, and the tunneling effect
M. V. Karasev
The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutati…