Topological meaning of Z2_2 numbers in time reversal invariant systems

We show that the Z$_2$ invariant, which classifies the topological properties of time reversal invariant insulators, has deep relationship with the global anomaly. Although the second Chern number is the basic topological invariant characterizing time reversal systems, we show that the relative phase between the Kramers doublet reduces the topological quantum number Z to Z$_2$.Comment: 4 pages, typos correcte

Neural-Network Vector Controller for Permanent-Magnet Synchronous Motor Drives: Simulated and Hardware-Validated Results

This paper focuses on current control in a permanentmagnet synchronous motor (PMSM). The paper has two main objectives: The first objective is to develop a neural-network (NN) vector controller to overcome the decoupling inaccuracy problem associated with conventional PI-based vector-control methods. The NN is developed using the full dynamic equation of a PMSM, and trained to implement optimal control based on approximate dynamic programming. The second objective is to evaluate the robust and adaptive performance of the NN controller against that of the conventional standard vector controller under motor parameter variation and dynamic control conditions by (a) simulating the behavior of a PMSM typically used in realistic electric vehicle applications and (b) building an experimental system for hardware validation as well as combined hardware and simulation evaluation. The results demonstrate that the NN controller outperforms conventional vector controllers in both simulation and hardware implementation

Phase Transformations in Binary Colloidal Monolayers

Phase transformations can be difficult to characterize at the microscopic level due to the inability to directly observe individual atomic motions. Model colloidal systems, by contrast, permit the direct observation of individual particle dynamics and of collective rearrangements, which allows for real-space characterization of phase transitions. Here, we study a quasi-two-dimensional, binary colloidal alloy that exhibits liquid-solid and solid-solid phase transitions, focusing on the kinetics of a diffusionless transformation between two crystal phases. Experiments are conducted on a monolayer of magnetic and nonmagnetic spheres suspended in a thin layer of ferrofluid and exposed to a tunable magnetic field. A theoretical model of hard spheres with point dipoles at their centers is used to guide the choice of experimental parameters and characterize the underlying materials physics. When the applied field is normal to the fluid layer, a checkerboard crystal forms; when the angle between the field and the normal is sufficiently large, a striped crystal assembles. As the field is slowly tilted away from the normal, we find that the transformation pathway between the two phases depends strongly on crystal orientation, field strength, and degree of confinement of the monolayer. In some cases, the pathway occurs by smooth magnetostrictive shear, while in others it involves the sudden formation of martensitic plates.Comment: 13 pages, 7 figures. Soft Matter Latex template was used. Published online in Soft Matter, 201

Integral geometry of complex space forms

We show how Alesker's theory of valuations on manifolds gives rise to an algebraic picture of the integral geometry of any Riemannian isotropic space. We then apply this method to give a thorough account of the integral geometry of the complex space forms, i.e. complex projective space, complex hyperbolic space and complex euclidean space. In particular, we compute the family of kinematic formulas for invariant valuations and invariant curvature measures in these spaces. In addition to new and more efficient framings of the tube formulas of Gray and the kinematic formulas of Shifrin, this approach yields a new formula expressing the volumes of the tubes about a totally real submanifold in terms of its intrinsic Riemannian structure. We also show by direct calculation that the Lipschitz-Killing valuations stabilize the subspace of invariant angular curvature measures, suggesting the possibility that a similar phenomenon holds for all Riemannian manifolds. We conclude with a number of open questions and conjectures.Comment: 68 pages; minor change

A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment

We present a preferential attachment growth model to obtain the distribution $P(K)$ of number of units $K$ in the classes which may represent business firms or other socio-economic entities. We found that $P(K)$ is described in its central part by a power law with an exponent $\phi=2+b/(1-b)$ which depends on the probability of entry of new classes, $b$. In a particular problem of city population this distribution is equivalent to the well known Zipf law. In the absence of the new classes entry, the distribution $P(K)$ is exponential. Using analytical form of $P(K)$ and assuming proportional growth for units, we derive $P(g)$, the distribution of business firm growth rates. The model predicts that $P(g)$ has a Laplacian cusp in the central part and asymptotic power-law tails with an exponent $\zeta=3$. We test the analytical expressions derived using heuristic arguments by simulations. The model might also explain the size-variance relationship of the firm growth rates.Comment: 19 pages 6 figures Applications of Physics in Financial Analysis, APFA

The Growth of Business Firms: Theoretical Framework and Empirical Evidence

We introduce a model of proportional growth to explain the distribution of business firm growth rates. The model predicts that the distribution is exponential in the central part and depicts an asymptotic power-law behavior in the tails with an exponent 3. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. In this article, we test the model at different levels of aggregation in the economy, from products to firms to countries, and we find that the model's predictions agree with empirical growth distributions and size-variance relationships.Comment: 22 pages, 5 Postscript figures, uses revtex4. to be published in Proc. Natl. Acad. Sci. (2005

A Generalized Preferential Attachment Model for Business Firms Growth Rates: I. Empirical Evidence

We introduce a model of proportional growth to explain the distribution $P(g)$ of business firm growth rates. The model predicts that $P(g)$ is Laplace in the central part and depicts an asymptotic power-law behavior in the tails with an exponent $\zeta=3$. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. We test the model at different levels of aggregation in the economy, from products, to firms, to countries, and we find that the its predictions are in good agreement with empirical evidence on both growth distributions and size-variance relationships.Comment: 8 pages, 4 figure

States interpolating between number and coherent states and their interaction with atomic systems

Using the eigenvalue definition of binomial states we construct new intermediate number-coherent states which reduce to number and coherent states in two different limits. We reveal the connection of these intermediate states with photon-added coherent states and investigate their non-classical properties and quasi-probability distributions in detail. It is of interest to note that these new states, which interpolate between coherent states and number states, neither of which exhibit squeezing, are nevertheless squeezed states. A scheme to produce these states is proposed. We also study the interaction of these states with atomic systems in the framework of the two-photon Jaynes-Cummings model, and describe the response of the atomic system as it varies between the pure Rabi oscillation and the collapse-revival mode and investigate field observables such as photon number distribution, entropy and the Q-function.Comment: 26 pages, 29 EPS figures, Latex, Accepted for publication in J.Phys.

Scalar Meson Spectroscopy with Lattice Staggered Fermions

With sufficiently light up and down quarks the isovector ($a_0$) and isosinglet ($f_0$) scalar meson propagators are dominated at large distance by two-meson states. In the staggered fermion formulation of lattice quantum chromodynamics, taste-symmetry breaking causes a proliferation of two-meson states that further complicates the analysis of these channels. Many of them are unphysical artifacts of the lattice approximation. They are expected to disappear in the continuum limit. The staggered-fermion fourth-root procedure has its purported counterpart in rooted staggered chiral perturbation theory (rSXPT). Fortunately, the rooted theory provides a strict framework that permits the analysis of scalar meson correlators in terms of only a small number of low energy couplings. Thus the analysis of the point-to-point scalar meson correlators in this context gives a useful consistency check of the fourth-root procedure and its proposed chiral realization. Through numerical simulation we have measured correlators for both the $a_0$ and $f_0$ channels in the ``Asqtad'' improved staggered fermion formulation in a lattice ensemble with lattice spacing $a = 0.12$ fm. We analyze those correlators in the context of rSXPT and obtain values of the low energy chiral couplings that are reasonably consistent with previous determinations.Comment: 23 pp., 3 figs., submitted to Phys. Rev.