M. V. Karasev

  1. Quantum Geometry and Quantum Mechanics of Integrable Systems.

    Authors: M. V. Karasev
    Subjects: Symplectic Geometry
    Abstract

    Quantum integrable systems and their classical counterparts are considered.
    We show that the symplectic structure and invariant tori of the classical
    system can be deformed by a quantization parameter $\hbar$ to produce a new
    (classical) integrable system. The new tori selected by the
    $\hbar$-equidistance rule represent the spectrum of the quantum system up to
    $O(\hbar^\infty)$ and are invariant under quantum dynamics in the long-time
    range $O(\hbar^{-\infty})$. The quantum diffusion over the deformed tori is
    described.

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