Exact time correlation functions for N classical Heisenberg spins in the `squashed' equivalent neighbor model

We present exact integral representations of the time-dependent spin-spin correlation functions for the classical Heisenberg N-spin `squashed' equivalent neighbor model, in which one spin is coupled via the Heisenberg exchange interaction with strength $J_1$ to the other N-1 spins, each of which is coupled via the Heisenberg exchange coupling with strength $J_2$ to the remaining N-2 spins. At low temperature T we find that the N spins oscillate in four modes, one of which is a central peak for a semi-infinite range of the values of the exchange coupling ratio. For the N=4 case of four spins on a squashed tetrahedron, detailed numerical evaluations of these results are presented. As $T\to\infty$, we calculate exactly the long-time asymptotic behavior of the correlation functions for arbitrary N, and compare our results with those obtained for three spins on an isosceles triangle.Comment: 9 pages, 8 figures, submitted to Phys. Rev.

On the Integrability of the Bukhvostov-Lipatov Model

The integrability of the Bukhvostov-Lipatov four-fermion model is investigated. It is shown that the classical model possesses a current of Lorentz spin 3, conserved both in the bulk and on the half-line for specific types of boundary actions. It is then established that the conservation law is spoiled at the quantum level -- a fact that might indicate that the quantum Bukhvostov-Lipatov model is not integrable, contrary to what was previously believed.Comment: 11 pages, 1 figure, LaTeX2e, AMS; new references adde

Time Correlation Functions of Three Classical Heisenberg Spins on an Isosceles Triangle and on a Chain: Strong Effects of Broken Symmetry

At arbitrary temperature $T$, we solve for the dynamics of single molecule magnets composed of three classical Heisenberg spins either on a chain with two equal exchange constants $J_1$, or on an isosceles triangle with a third, different exchange constant $J_2$. As T\rightrarrow\infty, the Fourier transforms and long-time asymptotic behaviors of the two-spin time correlation functions are evaluated exactly. The lack of translational symmetry on a chain or an isosceles triangle yields time correlation functions that differ strikingly from those on an equilateral trinagle with $J_1=J_2$. At low $T$, the Fourier transforms of the two autocorrelation functions with $J_1\ne J_2$ show one and four modes, respectively. For a semi-infinite $J_2/J_1$ range, one mode is a central peak. At the origin of this range, this mode has a novel scaling form.Comment: 9 pages, 14 figures, accepted for publication in Phys. Rev.

Medical education and research environment in Qatar: a new epoch for translational research in the Middle East

Recent advances in medical technology and key discoveries in biomedical research have the potential to improve human health in an unprecedented fashion. As a result, many of the Arab Gulf countries, particularly Qatar are devoting increasing resources toward establishing centers of excellence in biomedical research. However, there are challenges that must be overcome. The low profile of private medical institutions and their negligible endowments in the region are examples of such challenges. Business-type government controlled universities are not the solution for overcoming the challenges facing higher education and research programs in the Middle East

Is the classical Bukhvostov-Lipatov model integrable? A Painlevé analysis

In this work we apply the Weiss, Tabor and Carnevale integrability criterion (Painlev'e analysis) to the classical version of the two dimensional BukhvostovLipatov model. We are led to the conclusion that the model is not integrable classically, except at a trivial point where the theory can be described in terms of two non interacting sine-Gordon models. [email protected] y [email protected] I. INTRODUCTION In a remarkable paper [1], Bukhvostov and Lipatov were able to map the partition function for interacting instantons and anti-instantons of the O(3) non-linear oe model onto a two component scalar field theory defined by the Lagrangian L = 2 X i=1 1 2 @ OE i @ OE i \Gamma ¯ 2 cos( 1 OE 1 ) cos( 2 OE 2 ) : (1) They further showed that the quantum version of the model above is exactly solvable provided the couplings 1 , 2 are constrained by the following relation: 1 2 1 + 1 2 2 = 1 ß : (2) The integrability in this case was proved via the bosoniz..

Multisensor acoustical systems: Calibration and related problems

Nowadays, acoustic antennas are used in different application fields with the primary aim of detecting the presence and the position of acoustic sources. The uncertainty in the evaluation of the acoustic source position is related to the knowledge of right acoustic locations of the microphones in the array, which is different from the geometric ones and needs a suitable calibration procedure to be evaluated. This paper, after an analysis of the problems related to the calibration of acoustic antennas, proposes a dedicated strategy with the aim of assessing an optimized experimental setup guaranteeing the best uncertainty in the acoustic source location