PT symmetry and large-N models

Recently developed methods for PT-symmetric models can be applied to quantum-mechanical matrix and vector models. In matrix models, the calculation of all singlet wave functions can be reduced to the solution a one-dimensional PT-symmetric model. The large-N limit of a wide class of matrix models exists, and properties of the lowest-lying singlet state can be computed using WKB. For models with cubic and quartic interactions, the ground state energy appears to show rapid convergence to the large-N limit. For the special case of a quartic model, we find explicitly an isospectral Hermitian matrix model. The Hermitian form for a vector model with O(N) symmetry can also be found, and shows many unusual features. The effective potential obtained in the large-N limit of the Hermitian form is shown to be identical to the form obtained from the original PT-symmetric model using familiar constraint field methods. The analogous constraint field prescription in four dimensions suggests that PT-symmetric scalar field theories are asymptotically free.Comment: 15 pages, to be published in J. Phys. A special issue on Pseudo Hermitian Hamiltonians in Quantum Physic

Study of the Wealth Inequality in the Minority Game

To demonstrate the usefulness of physical approaches for the study of realistic economic systems, we investigate the inequality of players' wealth in one of the most extensively studied econophysical models, namely, the minority game (MG). We gauge the wealth inequality of players in the MG by a well-known measure in economics known as the modified Gini index. From our numerical results, we conclude that the wealth inequality in the MG is very severe near the point of maximum cooperation among players, where the diversity of the strategy space is approximately equal to the number of strategies at play. In other words, the optimal cooperation between players comes hand in hand with severe wealth inequality. We also show that our numerical results in the asymmetric phase of the MG can be reproduced semi-analytically using a replica method.Comment: 9 pages in revtex 4 style with 3 figures; minor revision with a change of title; to appear in PR

One Loop Graviton Self-Energy In A Locally De Sitter Background

The graviton tadpole has recently been computed at two loops in a locally de Sitter background. We apply intermediate results of this work to exhibit the graviton self-energy at one loop. This quantity is interesting both to check the accuracy of the first calculation and to understand the relaxation effect it reveals. In the former context we show that the self-energy obeys the appropriate Ward identity. We also show that its flat space limit agrees with the flat space result obtained by Capper in what should be the same gauge.Comment: 35 pages, plain TeX, 4 Postscript files, uses psfig.sty, revised June 1996 for publication in Physical Review

Decay of nuclear hyperpolarization in silicon microparticles

We investigate the low-field relaxation of nuclear hyperpolarization in undoped and highly doped silicon microparticles at room temperature following removal from high field. For nominally undoped particles, two relaxation time scales are identified for ambient fields above 0.2 mT. The slower, T_1s, is roughly independent of ambient field; the faster, T_1f, decreases with increasing ambient field. A model in which nuclear spin relaxation occurs at the particle surface via a two-electron mechanism is shown to be in good agreement with the experimental data, particularly the field-independence of T_1s. For boron-doped particles, a single relaxation time scale is observed. This suggests that for doped particles, mobile carriers and bulk ionized acceptor sites, rather than paramagnetic surface states, are the dominant relaxation mechanisms. Relaxation times for the undoped particles are not affected by tumbling in a liquid solution.Comment: related papers at http://marcuslab.harvard.ed

Emergent Time and the M5-Brane

We consider the maximal super-Yang-Mills theory in 5 Euclidean dimensions with SO(5) R-symmetry and 16 supersymmetries. We argue that the strong coupling limit of this theory (with a possible UV completion) has an emergent time dimension and gives a description of the 5+1 dimensional Lorentz invariant (2,0) theory of the M5-brane, compactified on a timelike circle with radius R=g^2/4\pi^2 . Our discussion involves issues of quantization of Euclidean theories without time.Comment: 1+40 page

Use of nanoporous ceramic membranes for carbon dioxide separation

Natural gas processes accounts for about 5.3 billion tonnes per year of carbon dioxide (CO2) emission to the atmosphere. At this rate of emission, the expectation will drastically rise if not curtailed. In order to achieve this, a cost-effective and environmental friendly technology is required. In recent times, membrane technology has been widely applied for CO2 removal from raw natural gas components. This article examines CO2 separation from natural gas, mainly methane (CH4), through a mesoporous composite membrane. A laboratory scale tubular silica membrane with a permeable length of 348 mm, I.D and O.D of 7 and 10 mm, respectively, was used in this experiment. Scanning electron microscopy (SEM) was used to analyze the morphology of the membrane. Single gas permeation of helium (He), CH4, nitrogen (N2), argon (Ar) and CO2 were determined at permeation temperature range between 25 and 100°C and feed gauge pressure of 0.05 to 5.0 barg. Before silica modification, He recorded the highest flow rate (0.3745 l/min) while CO2 recorded the least flow rate (0.1351 l/min) at 0.4 barg and 25°C. After silica modification, CO2 flow enhances significantly (3.1180 l/min at 1.0 barg) compared to CH4 (2.1200 l/min at the same gauge pressure) due to the influence of surface flow mechanism. Temperature variation described the applicability of Knudsen diffusion for He. A combination of viscous, surface and Knudsen diffusion transport mechanisms were obtained throughout the experiment. Membrane thickness was also calculated to be 2.5 × 10−4 m

The Correlation Functions of the XXZ Heisenberg Chain for Zero or Infinite Anisotropy and Random Walks of Vicious Walkers

The XXZ Heisenberg chain is considered for two specific limits of the anisotropy parameter: \Dl\to 0 and \Dl\to -\infty. The corresponding wave functions are expressed by means of the symmetric Schur functions. Certain expectation values and thermal correlation functions of the ferromagnetic string operators are calculated over the base of N-particle Bethe states. The thermal correlator of the ferromagnetic string is expressed through the generating function of the lattice paths of random walks of vicious walkers. A relationship between the expectation values obtained and the generating functions of strict plane partitions in a box is discussed. Asymptotic estimate of the thermal correlator of the ferromagnetic string is obtained in the limit of zero temperature. It is shown that its amplitude is related to the number of plane partitions.Comment: 22 pages, 1 figure, LaTe