For many classically chaotic systems it is believed that the quantum wave functions become uniformly distributed, that is the matrix elements of smooth observables tend to the phase space average of the observable. In this paper we study the ﬂuctuations of the matrix elements for the desymmetrized quantum cat map. We present a conjecture for the distribution of the normalized matrix elements, namely that their distribution is that of a certain weighted sum of traces of independent matrices in SU(2).
In the third century of the
Common Era (CE), when Rome dominated not only Europe, but also North Africa
and the Near East, it was able to deploy fifty legions throughout the empire. In this
forward defense strategy even the furthermost areas of the empire were secured by
the on-site presence of an adequate number of legions of the Roman army.
However, the empire had lost much of its muscle by the fourth century CE and the
forces of Rome had diminished to only about twenty-five legions.
Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: An ’average information’ restricted
maximum likelihood algorithm
for estimating reduced rank genetic
covariance matrices or
covariance functions for animal models
with equal design matrices