Spectral statistics for quantized skew translations on the torus
نویسندگان
چکیده
We study the spectral statistics for quantized skew translations on the torus, which are ergodic but not mixing for irrational parameters. It is shown explicitly that in this case the level– spacing distribution and other common spectral statistics, like the number variance, do not exist in the semiclassical limit. ∗ E-mail address: [email protected] ∗∗ E-mail address: [email protected]
منابع مشابه
Quantization of a Class of Piecewise Affine Transformations on the Torus
We present a unified framework for the quantization of a family of discrete dynamical systems of varying degrees of “chaoticity”. The systems to be quantized are piecewise affine maps on the two-torus, viewed as phase space, and include the automorphisms, translations and skew translations. We then treat some discontinuous transformations such as the Baker map and the sawtooth-like maps. Our ap...
متن کاملChaos, Quantization and the Classical Limit on the Torus
The algebraic and the canonical approaches to the quantization of a class of classical symplectic dynamical systems on the two-torus are presented in a simple unified framework. This allows for ready comparison between the two very different approaches and is well adapted to the study of the semi-classical behaviour of the resulting models. Ergodic translations and skew translations, as well as...
متن کاملQuantum Unique Ergodicity for Parabolic Maps
We study the ergodic properties of quantized ergodic maps of the torus. It is known that these satisfy quantum ergodicity: For almost all eigenstates, the expectation values of quantum observables converge to the classical phase-space average with respect to Liouville measure of the corresponding classical observable. The possible existence of any exceptional subsequences of eigenstates is an i...
متن کاملA Statistical Study of two Diffusion Processes on Torus and Their Applications
Diffusion Processes such as Brownian motions and Ornstein-Uhlenbeck processes are the classes of stochastic processes that have been investigated by researchers in various disciplines including biological sciences. It is usually assumed that the outcomes of these processes are laid on the Euclidean spaces. However, some data in physical, chemical and biological phenomena indicate that they cann...
متن کاملOn the Canonical-Based Goodness-of-fit Tests for Multivariate Skew-Normality
It is well-known that the skew-normal distribution can provide an alternative model to the normal distribution for analyzing asymmetric data. The aim of this paper is to propose two goodness-of-fit tests for assessing whether a sample comes from a multivariate skew-normal (MSN) distribution. We address the problem of multivariate skew-normality goodness-of-fit based on the empirical Laplace tra...
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 1999