Lyapunov instabilities in lattices of interacting classical spins at infinite temperature

We numerically investigate Lyapunov instabilities for one-, two- and three-dimensional lattices of interacting classical spins at infinite temperature. We obtain the largest Lyapunov exponents for a very large variety of nearest-neighbor spin-spin interactions and complete Lyapunov spectra in a few selected cases. We investigate the dependence of the largest Lyapunov exponents and whole Lyapunov spectra on the lattice size and find that both quickly become size-independent. Finally, we analyze the dependence of the largest Lyapunov exponents on the anisotropy of spin-spin interaction with the particular focus on the difference between bipartite and nonbipartite lattices

Analog Computer Research

Contains reports on two research projects

To Issue or Not to Issue: Analysis of the Business Method Patent Controvery on the Internet

The author argues that in time business method patents will promote competition and innovation on the Internet. He begins by tracing the history, goals, and criteria of patent law in general, and then discusses the birth of the BMP, reviews a sample of recently issued BMPs, and summarizes the various arguments that undercut and support the advent of the BMP. After reviewing the arguments against Internet-based BMPs, the author asserts that although various and sometimes random, scholarly criticisms can be placed into three broad classifications: quality, efficiency, and consistency. Balancing these arguments, the author argues that although the consistency arguments have merit, they ignore the realities of the Internet business sector

Bell's theorem as a signature of nonlocality: a classical counterexample

For a system composed of two particles Bell's theorem asserts that averages of physical quantities determined from local variables must conform to a family of inequalities. In this work we show that a classical model containing a local probabilistic interaction in the measurement process can lead to a violation of the Bell inequalities. We first introduce two-particle phase-space distributions in classical mechanics constructed to be the analogs of quantum mechanical angular momentum eigenstates. These distributions are then employed in four schemes characterized by different types of detectors measuring the angular momenta. When the model includes an interaction between the detector and the measured particle leading to ensemble dependencies, the relevant Bell inequalities are violated if total angular momentum is required to be conserved. The violation is explained by identifying assumptions made in the derivation of Bell's theorem that are not fulfilled by the model. These assumptions will be argued to be too restrictive to see in the violation of the Bell inequalities a faithful signature of nonlocality.Comment: Extended manuscript. Significant change

Quantum analogues of Hardy's nonlocality paradox

Hardy's nonlocality is a "nonlocality proof without inequalities": it exemplifies that quantum correlations can be qualitatively stronger than classical correlations. This paper introduces variants of Hardy's nonlocality in the CHSH scenario which are realized by the PR-box, but not by quantum correlations. Hence this new kind of Hardy-type nonlocality is a proof without inequalities showing that superquantum correlations can be qualitatively stronger than quantum correlations.Comment: minor fixe

Tuberculosis and gender: exploring the patterns in a case control study in Malawi.

BACKGROUND: In many populations there is an excess of tuberculosis in young women and older men. We explored possible explanations for these patterns, concentrating on human immunodeficiency virus (HIV) status, pregnancy, smoking, cooking smoke exposure, contact with tuberculosis cases within the household or outside, and gender differences in health service usage and diagnostic delay. DESIGN: Case control study in Karonga District, Malawi. METHODS: Cases were new tuberculosis patients with bacteriological or histological evidence of tuberculosis. Controls were selected in the community using field-based random sampling. RESULTS: The study included 598 tuberculosis cases and 992 controls, with an excess of tuberculosis in young females and older males. This was more marked in HIV-positive individuals. HIV infection was a similarly strong risk factor for tuberculosis in both men and women. Tuberculosis was associated with having a family or household contact with tuberculosis for both men and women. For women, but not men, contacts outside the close family and household were also a risk factor for tuberculosis. Tuberculosis was not associated with current or recent pregnancy, or with smoking or smoke exposure. There were no differences between men and women in health service usage or delay. CONCLUSIONS: In this population, HIV infection and contacts with known tuberculosis patients are important determinants of the gender distribution of cases

Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2

We show that macroscopic nonintegrable lattices of spins 1/2, which are often considered to be chaotic, do not exhibit the basic property of classical chaotic systems, namely, exponential sensitivity to small perturbations. We compare chaotic lattices of classical spins and nonintegrable lattices of spins 1/2 in terms of their magnetization responses to imperfect reversal of spin dynamics known as Loschmidt echo. In the classical case, magnetization exhibits exponential sensitivity to small perturbations of Loschmidt echoes, which is characterized by twice the value of the largest Lyapunov exponent of the system. In the case of spins 1/2, magnetization is only power-law sensitive to small perturbations. Our findings imply that it is impossible to define Lyapunov exponents for lattices of spins 1/2 even in the macroscopic limit. At the same time, the above absence of exponential sensitivity to small perturbations is an encouraging news for the efforts to create quantum simulators. The power-law sensitivity of spin 1/2 lattices to small perturbations is predicted to be measurable in nuclear magnetic resonance experiments.Comment: 12 pages, 8 figures, minor changes, new reference