Wither the sliding Luttinger liquid phase in the planar pyrochlore

Using series expansion based on the flow equation method we study the zero temperature properties of the spin-1/2 planar pyrochlore antiferromagnet in the limit of strong diagonal coupling. Starting from the limit of decoupled crossed dimers we analyze the evolution of the ground state energy and the elementary triplet excitations in terms of two coupling constants describing the inter dimer exchange. In the limit of weakly coupled spin-1/2 chains we find that the fully frustrated inter chain coupling is critical, forcing a dimer phase which adiabatically connects to the state of isolated dimers. This result is consistent with findings by O. Starykh, A. Furusaki and L. Balents (Phys. Rev. B 72, 094416 (2005)) which is inconsistent with a two-dimensional sliding Luttinger liquid phase at finite inter chain coupling.Comment: 6 pages, 4 Postscript figures, 1 tabl

The functional integral with unconditional Wiener measure for anharmonic oscillator

In this article we propose the calculation of the unconditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. In such a case we can profit from the representation of the integral in question by the parabolic cylinder functions. We show that in such a case the series expansions are uniformly convergent and we find recurrence relations for the Wiener functional integral in the $N$ - dimensional approximation. In continuum limit we find that the generalized Gelfand - Yaglom differential equation with solution yields the desired functional integral (similarly as the standard Gelfand - Yaglom differential equation yields the functional integral for linear harmonic oscillator).Comment: Source file which we sent to journa

Generating Functional for Strong and Nonleptonic Weak Interactions

The generating functional for Green functions of quark currents is given in closed form to next-to-leading order in the low-energy expansion for chiral SU(3), including one-loop amplitudes with up to three meson propagators. Matrix elements and form factors for strong and nonleptonic weak processes with at most six external states can be extracted from this functional by performing three-dimensional flavour traces. To implement this procedure, a Mathematica program is provided that evaluates amplitudes with at most six external mesons, photons (real or virtual) and virtual W (semileptonic form factors). The program is illustrated with several examples that can be compared with existing calculations.Comment: 26 pages; references added, comparison with other programs added, small changes in the text, version to appear in JHE

Towards generalized measures grasping CA dynamics

In this paper we conceive Lyapunov exponents, measuring the rate of separation between two initially close configurations, and Jacobians, expressing the sensitivity of a CA's transition function to its inputs, for cellular automata (CA) based upon irregular tessellations of the n-dimensional Euclidean space. Further, we establish a relationship between both that enables us to derive a mean-field approximation of the upper bound of an irregular CA's maximum Lyapunov exponent. The soundness and usability of these measures is illustrated for a family of 2-state irregular totalistic CA

Spontaneous emergence of spatial patterns ina a predator-prey model

We present studies for an individual based model of three interacting populations whose individuals are mobile in a 2D-lattice. We focus on the pattern formation in the spatial distributions of the populations. Also relevant is the relationship between pattern formation and features of the populations' time series. Our model displays travelling waves solutions, clustering and uniform distributions, all related to the parameters values. We also observed that the regeneration rate, the parameter associated to the primary level of trophic chain, the plants, regulated the presence of predators, as well as the type of spatial configuration.Comment: 17 pages and 15 figure

A new Method for Computing One-Loop Integrals

We present a new program package for calculating one-loop Feynman integrals, based on a new method avoiding Feynman parametrization and the contraction due to Passarino and Veltman. The package is calculating one-, two- and three-point functions both algebraically and numerically to all tensor cases. This program is written as a package for Maple. An additional Mathematica version is planned later.Comment: 12 pages Late

Field theory of the inverse cascade in two-dimensional turbulence

A two-dimensional fluid, stirred at high wavenumbers and damped by both viscosity and linear friction, is modeled by a statistical field theory. The fluid's long-distance behavior is studied using renormalization-group (RG) methods, as begun by Forster, Nelson, and Stephen [Phys. Rev. A 16, 732 (1977)]. With friction, which dissipates energy at low wavenumbers, one expects a stationary inverse energy cascade for strong enough stirring. While such developed turbulence is beyond the quantitative reach of perturbation theory, a combination of exact and perturbative results suggests a coherent picture of the inverse cascade. The zero-friction fluctuation-dissipation theorem (FDT) is derived from a generalized time-reversal symmetry and implies zero anomalous dimension for the velocity even when friction is present. Thus the Kolmogorov scaling of the inverse cascade cannot be explained by any RG fixed point. The beta function for the dimensionless coupling ghat is computed through two loops; the ghat^3 term is positive, as already known, but the ghat^5 term is negative. An ideal cascade requires a linear beta function for large ghat, consistent with a Pad\'e approximant to the Borel transform. The conjecture that the Kolmogorov spectrum arises from an RG flow through large ghat is compatible with other results, but the accurate k^{-5/3} scaling is not explained and the Kolmogorov constant is not estimated. The lack of scale invariance should produce intermittency in high-order structure functions, as observed in some but not all numerical simulations of the inverse cascade. When analogous RG methods are applied to the one-dimensional Burgers equation using an FDT-preserving dimensional continuation, equipartition is obtained instead of a cascade--in agreement with simulations.Comment: 16 pages, 3 figures, REVTeX 4. Material added on energy flux, intermittency, and comparison with Burgers equatio

Extended Heat-Fluctuation Theorems for a System with Deterministic and Stochastic Forces

Heat fluctuations over a time \tau in a non-equilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components: a Brownian particle dragged through a fluid by a harmonic potential which is moved with constant velocity. Using a Langevin equation, we find the exact Fourier transform of the distribution of these fluctuations for all \tau. By a saddle-point method we obtain analytical results for the inverse Fourier transform, which, for not too small \tau, agree very well with numerical results from a sampling method as well as from the fast Fourier transform algorithm. Due to the interaction of the deterministic part of the motion of the particle in the mechanical potential with the stochastic part of the motion caused by the fluid, the conventional heat fluctuation theorem is, for infinite and for finite \tau, replaced by an extended fluctuation theorem that differs noticeably and measurably from it. In particular, for large fluctuations, the ratio of the probability for absorption of heat (by the particle from the fluid) to the probability to supply heat (by the particle to the fluid) is much larger here than in the conventional fluctuation theorem.Comment: 23 pages, 6 figures. Figures are now in color, Eq. (67) was corrected and a footnote was added on the d-dimensional cas

Pseudo-random operators of the circular ensembles

We demonstrate quantum algorithms to implement pseudo-random operators that closely reproduce statistical properties of random matrices from the three universal classes: unitary, symmetric, and symplectic. Modified versions of the algorithms are introduced for the less experimentally challenging quantum cellular automata. For implementing pseudo-random symplectic operators we provide gate sequences for the unitary part of the time-reversal operator.Comment: 5 pages, 4 figures, to be published PR