Quantum Transport on KAM Tori

Details Quantum Transport on KAM Tori Quantum Transport on KAM Tori

1998-12-09

arxiv.org/abs/math-ph/9812006v1

Physics

Mathematical Physics

21 pages

Scientific paper

10.1007/s002200050670

Although quantum tunneling between phase space tori occurs, it is suppressed in the semiclassical limit $\hbar\searrow 0$ for the Schr\"{o}dinger equation of a particle in $\bR^d$ under the influence of a smooth periodic potential. In particular this implies that the distribution of quantum group velocities near energy $E$ converges to the distribution of the classical asymptotic velocities near $E$, up to a term of the order $\cO(1/\sqrt{E})$.

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