Quantum chaos: an introduction via chains of interacting spins-1/2

We introduce aspects of quantum chaos by analyzing the eigenvalues and the eigenstates of quantum many-body systems. The properties of quantum systems whose classical counterparts are chaotic differ from those whose classical counterparts are not chaotic. The spectrum of the first exhibits repulsion of the energy levels. This is one of the main signatures of quantum chaos. We show how level repulsion develops in one-dimensional systems of interacting spins 1/2 which are devoid of random elements and involve only two-body interactions. In addition to the statistics of the eigenvalues, we analyze how the structure of the eigenstates may indicate chaos. The programs used to obtain the data are available online.Comment: 7 pages, 3 figure

ОСОБЕННОСТИ ЛИЧНОСТНОГО АДАПТАЦИОННОГО ПОТЕНЦИАЛА У ЛИЦ СРЕДНЕГО ВОЗРАСТА В УСЛОВИЯХ СОЦИАЛЬНОЙ ИЗОЛЯЦИИ, СОВЕРШИВШИХ ПРЕСТУПЛЕНИЕ ПРОТИВ ЛИЧНОСТИ

The article discusses theoretical and applied issues of studying the adaptive potential of middle-aged people who are in conditions of social isolation. В статье рассматриваются теоретические и прикладные вопросы изучения адаптационного потенциала у лиц среднего возраста, находящихся в условиях социальной изоляции.

The multifrequency Siberian Radioheliograph

The 10-antenna prototype of the multifrequency Siberian radioheliograph is described. The prototype consists of four parts: antennas with broadband front-ends, analog back-ends, digital receivers and a correlator. The prototype antennas are mounted on the outermost stations of the Siberian Solar Radio Telescope (SSRT) array. A signal from each antenna is transmitted to a workroom by an analog fiber optical link, laid in an underground tunnel. After mixing, all signals are digitized and processed by digital receivers before the data are transmitted to the correlator. The digital receivers and the correlator are accessible by the LAN. The frequency range of the prototype is from 4 to 8 GHz. Currently the frequency switching observing mode is used. The prototype data include both circular polarizations at a number of frequencies given by a list. This prototype is the first stage of the multifrequency Siberian radioheliograph development. It is assumed that the radioheliograph will consist of 96 antennas and will occupy stations of the West-East-South subarray of the SSRT. The radioheliograph will be fully constructed in autumn of 2012. We plan to reach the brightness temperature sensitivity about 100 K for the snapshot image, a spatial resolution up to 13 arcseconds at 8 GHz and polarization measurement accuracy about a few percent. First results with the 10-antenna prototype are presented of observations of solar microwave bursts. The prototype abilities to estimate source size and locations at different frequencies are discussed