Quantum entanglement entropy and classical mutual information in long-range harmonic oscillators

We study different aspects of quantum von Neumann and R\'enyi entanglement entropy of one dimensional long-range harmonic oscillators that can be described by well-defined non-local field theories. We show that the entanglement entropy of one interval with respect to the rest changes logarithmically with the number of oscillators inside the subsystem. This is true also in the presence of different boundary conditions. We show that the coefficients of the logarithms coming from different boundary conditions can be reduced to just two different universal coefficients. We also study the effect of the mass and temperature on the entanglement entropy of the system in different situations. The universality of our results is also confirmed by changing different parameters in the coupled harmonic oscillators. We also show that more general interactions coming from general singular Toeplitz matrices can be decomposed to our long-range harmonic oscillators. Despite the long-range nature of the couplings we show that the area law is valid in two dimensions and the universal logarithmic terms appear if we consider subregions with sharp corners. Finally we study analytically different aspects of the mutual information such as its logarithmic dependence to the subsystem, effect of mass and influence of the boundary. We also generalize our results in this case to general singular Toeplitz matrices and higher dimensions.Comment: 21 pages, 26 figure

First passage time processes and subordinated SLE

We study the first passage time processes of anomalous diffusion on self similar curves in two dimensions. The scaling properties of the mean square displacement and mean first passage time of the ballistic motion, fractional Brownian motion and subordinated walk on different fractal curves (loop erased random walk, harmonic explorer and percolation front) are derived. We also define natural parametrized subordinated Schramm Loewner evolution (NS-SLE) as a mathematical tool that can model diffusion on fractal curves. The scaling properties of the mean square displacement and mean first passage time for NS-SLE are obtained by numerical means.Comment: 8 pages, 3 figure

Complications leading to hospitalization due to consumption of anti-TB drugs in patients with tuberculosis in Gorgan, Iran (2007-12)

Background and Objective: Anti tuberculosis drugs therapy is the most effective method for controling the tuberculosis (TB). Early detection and appropriate treatment can prevent the TB-drug resistance. This study was carried out to determine the complications leading to hospitalization due to consumption of anti-TB drugs in patients with tuberculosis. Methods: In this descriptive-analytic study, 1550 records of patients with TB in urban and rural health centers of Gorgan, north of Iran were assessed during 2007-12. Checklist consists of demographic and clinical data for each patient was recorded in a questionare. Results: 44 cases experienced the complications of anti-TB drugs. 27 (61.4%) of cases with complications were women. 77.3% and 22.7% of patients affected with pulmonary and extra pulmonary tuberculosis,respectively. 38.6% of patients were diabetic. The hepatic complication was seen in 37 cases (84.1%). Skin and other complications were seen in 5 and 2 cases, respectively. There was not any relationship between drug complications and other disases. Conclusion: Hepatic damage is the most common complication leading to hospitalization in tuberculosis patients using anti-TB drugs. Keywords: Tuberculosis, Anti-TB drug, Live