Cyclic and ruled Lagrangian surfaces in complex Euclidean space

We study those Lagrangian surfaces in complex Euclidean space which are foliated by circles or by straight lines. The former, which we call cyclic, come in three types, each one being described by means of, respectively, a planar curve, a Legendrian curve of the 3-sphere or a Legendrian curve of the anti de Sitter 3-space. We also describe ruled Lagrangian surfaces. Finally we characterize those cyclic and ruled Lagrangian surfaces which are solutions to the self-similar equation of the Mean Curvature Flow. Finally, we give a partial result in the case of Hamiltonian stationary cyclic surfaces

Partonic effects on anisotropic flows at RHIC

We report recent results from a multiphase transport (AMPT) model on the azimuthal anisotropies of particle momentum distributions in heavy ion collisions at the Relativistic Heavy Ion Collider. These include higher-order anisotropic flows and their scaling, the rapidity dependence of anisotropic flows, and the elliptic flow of charm quarks.Comment: 7 pages, 5 figures, talk given at "Hot Quarks 2004", July 18-24, 2004, Taos Valley, NM, US

Demonstration of the difference Casimir force for samples with different charge carrier densities

A measurement of the Casimir force between a gold coated sphere and two Si plates of different carrier densities is performed using a high vacuum based atomic force microscope. The results are compared with the Lifshitz theory and good agreement is found. Our experiment demonstrates that by changing the carrier density of the semiconductor plate by several orders of magnitude it is possible to modify the Casimir interaction. This result may find applications in nanotechnology.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

Leading Chiral Corrections to the Nucleon Generalized Parton Distributions

Using heavy baryon chiral perturbation theory we study the leading chiral corrections to the complete set of nucleon generalized parton distributions (GPDs). We compute the leading quark mass and momentum transfer dependence of the moments of nucleon GPDs through the nucleon off-forward twist-2 matrix elements. These results are then applied to get insight on the GPDs and their impact parameter space distributions.Comment: 26 pages, 2 figures; minor revisio

Charge-density-wave order parameter of the Falicov-Kimball model in infinite dimensions

In the large-U limit, the Falicov-Kimball model maps onto an effective Ising model, with an order parameter described by a BCS-like mean-field theory in infinite dimensions. In the small-U limit, van Dongen and Vollhardt showed that the order parameter assumes a strange non-BCS-like shape with a sharp reduction near T approx T_c/2. Here we numerically investigate the crossover between these two regimes and qualitatively determine the order parameter for a variety of different values of U. We find the overall behavior of the order parameter as a function of temperature to be quite anomalous.Comment: (5 pages, 3 figures, typeset with ReVTeX4

Quenching across quantum critical points: role of topological patterns

We introduce a one-dimensional version of the Kitaev model consisting of spins on a two-legged ladder and characterized by Z_2 invariants on the plaquettes of the ladder. We map the model to a fermionic system and identify the topological sectors associated with different Z_2 patterns in terms of fermion occupation numbers. Within these different sectors, we investigate the effect of a linear quench across a quantum critical point. We study the dominant behavior of the system by employing a Landau-Zener-type analysis of the effective Hamiltonian in the low-energy subspace for which the effective quenching can sometimes be non-linear. We show that the quenching leads to a residual energy which scales as a power of the quenching rate, and that the power depends on the topological sectors and their symmetry properties in a non-trivial way. This behavior is consistent with the general theory of quantum quenching, but with the correlation length exponent \nu being different in different sectors.Comment: 5 pages including 2 figures; this is the published versio

Approximating Multilinear Monomial Coefficients and Maximum Multilinear Monomials in Multivariate Polynomials

This paper is our third step towards developing a theory of testing monomials in multivariate polynomials and concentrates on two problems: (1) How to compute the coefficients of multilinear monomials; and (2) how to find a maximum multilinear monomial when the input is a $\Pi\Sigma\Pi$ polynomial. We first prove that the first problem is \#P-hard and then devise a $O^*(3^ns(n))$ upper bound for this problem for any polynomial represented by an arithmetic circuit of size $s(n)$. Later, this upper bound is improved to $O^*(2^n)$ for $\Pi\Sigma\Pi$ polynomials. We then design fully polynomial-time randomized approximation schemes for this problem for $\Pi\Sigma$ polynomials. On the negative side, we prove that, even for $\Pi\Sigma\Pi$ polynomials with terms of degree $\le 2$, the first problem cannot be approximated at all for any approximation factor $\ge 1$, nor {\em "weakly approximated"} in a much relaxed setting, unless P=NP. For the second problem, we first give a polynomial time $\lambda$-approximation algorithm for $\Pi\Sigma\Pi$ polynomials with terms of degrees no more a constant $\lambda \ge 2$. On the inapproximability side, we give a $n^{(1-\epsilon)/2}$ lower bound, for any $\epsilon >0,$ on the approximation factor for $\Pi\Sigma\Pi$ polynomials. When terms in these polynomials are constrained to degrees $\le 2$, we prove a $1.0476$ lower bound, assuming $P\not=NP$; and a higher $1.0604$ lower bound, assuming the Unique Games Conjecture

A new polymorphic material? Structural degeneracy of ZrMn_2

Based on density functional calculations, we propose that ZrMn_2 is a polymorphic material. We predict that at low temperatures the cubic C15, and the hexagonal C14 and C36 structures of the Laves phase compound ZrMn_2 are nearly equally stable within 0.3 kJmol^{-1} or 30 K. This degeneracy occurs when the Mn atoms magnetize spontaneously in a ferromagnetic arrangement forming the states of lowest energy. From the temperature dependent free energies at T approx 160K we predict a transition from the most stable C15 to the C14 structure, which is the experimentally observed structure at elevated temperatures.Comment: 4 pages, 3 figure

Experimental procedures for precision measurements of the Casimir force with an Atomic Force Microscope

Experimental methods and procedures required for precision measurements of the Casimir force are presented. In particular, the best practices for obtaining stable cantilevers, calibration of the cantilever, correction of thermal and mechanical drift, measuring the contact separation, sphere radius and the roughness are discussed.Comment: 14 pages, 7 figure