Quantum Geometry and Quantum Mechanics of Integrable Systems.
Пнд, 08/17/2009 - 18:30 — SomNambul
link: http://arxiv.org/abs/0908.2048
Abstract
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. The analytic apparatus uses quantum action-angle coordinates
explicitly constructed by an $\hbar$-deformation of the classical
action-angles.
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