 9462 Degli Esposti M., Graffi S., Isola S.
 Classical Limit of the Quantized Hyperbolic Toral Automorphisms
(100K, AmSTeX)
Mar 10, 94

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. The canonical quantization of any hyperbolic symplectomorphism
$A$ of the 2torus yields a periodic unitary operator on a $N$dimensional
Hilbert space,
$N=\frac1{h}$. We prove that this quantum system becomes ergodic and mixing at
the classical limit ($N\to\infty $, $N$ prime) which can be interchanged with
the timeaverage limit. The recovery of the stochastic behaviour out of a
periodic one is based on the same mechanism under which the uniform
distribution of the classical periodic orbits reproduces the Lebesgue measure:
the Wigner functions of the eigenstates, supported on the classical periodic
orbits, are indeed proved to become uniformly spread in phase space.
 Files:
9462.tex