Noncommutative Algebras, Nano-Structures, and Quantum Dynamics Generated by Resonances

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dc.creatorKarasev, Mikhail
dc.date2004-12-30
dc.date2005-05-27
dc.date.accessioned2026-07-07T05:15:42Z
dc.date.available2026-07-07T05:15:42Z
dc.descriptionWe observe ``quantum'' properties of resonance equilibrium points and resonance univariant submanifolds in the phase space. Resonances between Birkhoff or Floquet--Lyapunov frequencies generate quantum algebras with polynomial commutation relations. Irreducible representations and coherent states of these algebras correspond to certain quantum nano-structure near the classical resonance motion. Based on this representation theory and nano-geometry, for equations of Schrödinger or wave type in various regimes and zones (up to quantum chaos borders) we describe the resonance spectral and long-time asymptotics, resonance localization and focusing, resonance adiabatic and spin-like effects. We discuss how the mathematical phase space nano-structures relate to physical nanoscale objects like dots, quantum wires, etc. We also demonstrate that even in physically macroscale Helmholtz channels the resonance implies a specific quantum character of classical wave propagation.
dc.descriptionLatex, 60pages, Part II added, minor corrections to Part I
dc.identifierhttps://arxiv.org/abs/math/0412542
dc.identifierhttp://arxiv.org/abs/math/0412542
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73723
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subject34E20, 35Lxx, 81Qxx
dc.titleNoncommutative Algebras, Nano-Structures, and Quantum Dynamics Generated by Resonances
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