Distribution of Resonances for Open Quantum Maps Stéphane Nonnenmacher and Maciej Zworski
نویسندگان
چکیده
1.1. Statement of the results. In this note we analyze simple models of classical chaotic open systems and of their quantizations. They provide a numerical confirmation of the fractal Weyl law for the density of quantum resonances of such systems. The exponent in that law is related to the dimension of the classical repeller of the system. In a simplified model, a rigorous argument gives the full resonance spectrum, which satisfies the fractal Weyl law. Our model is similar to models recently studied in atomic and mesoscopic physics (see §2.4 below). Before stating the main result we remark that in this paper we use mathematician’s notation h for what the physicists call ~. That is partly to stress that our h is a small parameter in asymptotic analysis, not necessarily interpreted as the Planck constant.
منابع مشابه
From open quantum systems to open quantum maps
In this paper we show that for a class of open quantum systems satisfying a natural dynamical assumption (see §2.2) the study of the resolvent, and hence of scattering, and of resonances, can be reduced, in the semiclassical limit, to the study of open quantum maps, that is of finite dimensional quantizations of canonical relations obtained by truncation of symplectomorphisms derived from the c...
متن کاملFractal Weyl laws for chaotic open systems.
We present a conjecture relating the density of quantum resonances for an open chaotic system to the fractal dimension of the associated classical repeller. Mathematical arguments justifying this conjecture are discussed. Numerical evidence based on computation of resonances of systems of n disks on a plane are presented supporting this conjecture. The result generalizes the Weyl law for the de...
متن کاملQuantum Resonances in Chaotic Scattering
This letter summarizes numerical results from [1] which show that in quantum systems with chaotic classical dynamics, the number of scattering resonances near an energy E scales like h̄− D(KE)+1 2 . Here, KE denotes the subset of the classical energy surface {H = E} which stays bounded for all time under the flow of H and D (KE) denotes its fractal dimension. Since the number of bound states in ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008