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1.
Masaki Hirata Benoît Saussol Sandro Vaienti 《Communications in Mathematical Physics》1999,206(1):33-55
In this paper we provide general estimates for the errors between the distribution of the first, and more generally, the K
th return time (suitably rescaled) and the Poisson law for measurable dynamical systems. In the case that the system exhibits
strong mixing properties, these bounds are explicitly expressed in terms of the speed of mixing. Using these approximations,
the Poisson law is finally proved to hold for a large class of non hyperbolic systems on the interval.
Received: 4 August 1998 / Accepted: 9 March 1999 相似文献
2.
Recently, several authors studied small quantum systems weakly coupled to free boson or fermion fields at positive temperature.
All the rigorous approaches we are aware of employ complex deformations of Liouvillians or Mourre theory (the infinitesimal
version of the former). We present an approach based on polymer expansions of statistical mechanics. Despite the fact that
our approach is elementary, our results are slightly sharper than those contained in the literature up to now. We show that,
whenever the small quantum system is known to admit a Markov approximation (Pauli master equation aka Lindblad equation) in the weak coupling limit, and the Markov approximation is exponentially mixing, then the weakly coupled
system approaches a unique invariant state that is perturbatively close to its Markov approximation. 相似文献