Abrupt transition in a sandpile model

We present a fixed energy sandpile (FES) model which, by increasing the initial energy,undergoes, at the level of individual configurations, a discontinuous transition.The model is obtained by modifying the toppling procedure in the BTW rules: the energy transfer from a toppling site takes place only to neighbouring sites with less energy (negative gradient constraint) and with a time ordering (asynchronous). The model is minimal in the sense that removing either of the two above mentioned constraints (negative gradient or time ordering) the abrupt transition goes over to a continuous transition as in the usual BTW case. Therefore the proposed model offers an unique possibility to explore at the microscopic level the basic mechanisms underlying discontinuous transitions.Comment: 7 pages, 5 figure

The photon polarization in B -> X gamma in the standard model

The standard model prediction for the $B\to X_{s,d}\gamma$ decay amplitude with a right-handed photon is believed to be tiny, suppressed by $m_{s,d}/m_b$, compared to the amplitude with a left-handed photon. We show that this suppression is fictitious: in inclusive decays, the ratio of these two amplitudes is only suppressed by $g_s/(4\pi)$, and in exclusive decays by $\Lambda_{QCD}/m_b$. The suppression is not stronger in $B\to X_d\gamma$ decays than it is in $B\to X_s\gamma$. We estimate that the time dependent CP asymmetries in $B\to K^*\gamma$, $\rho\gamma$, $K_S\pi^0\gamma$, and $\pi^+\pi^-\gamma$ are of order 0.1 and that they have significant uncertainties.Comment: Clarifications in the exclusive section, references adde

Systems with Multiplicative Noise: Critical Behavior from KPZ Equation and Numerics

We show that certain critical exponents of systems with multiplicative noise can be obtained from exponents of the KPZ equation. Numerical simulations in 1d confirm this prediction, and yield other exponents of the multiplicative noise problem. The numerics also verify an earlier prediction of the divergence of the susceptibility over an entire range of control parameter values, and show that the exponent governing the divergence in this range varies continuously with control parameter.Comment: Four pages (In Revtex format) with 4 figures (in Postcript

Reparameterization Invariance to all Orders in Heavy Quark Effective Theory

Heavy Quark Effective Theory splits a heavy quark momentum into a large fixed momentum and a variable residual momentum, p = m_Q v + k. It thereby suffers a redundancy of description corresponding to small changes in the choice of the fixed velocity, v. The fact that full QCD is manifestly v-independent should lead to a non-trivial constraint on the form of the effective theory, known as Reparameterization Invariance. For spin-1/2 quarks, the precise form of the constraint and its solution at the level of the effective lagrangian have proven to be rather subtle, and the original proposal by Luke and Manohar has been questioned. In this paper I employ a version of Heavy Quark Effective Theory containing the ``anti-particle'' field as a non-propagating auxiliary field, which greatly simplifies keeping track of v-dependence. This permits a very simple derivation of Reparameterization Invariance from first principles. The auxiliary field can also be integrated out to return to the standard formulation of the effective theory, but with the effective lagrangian now satisfying the full reparameterization constraint. I compare this result with earlier proposals.Comment: 12 pages, LaTex. Important and confusing typographical error in eq. (15) corrected. To appear in Phys. Rev.

The Entropy of a Binary Hidden Markov Process

The entropy of a binary symmetric Hidden Markov Process is calculated as an expansion in the noise parameter epsilon. We map the problem onto a one-dimensional Ising model in a large field of random signs and calculate the expansion coefficients up to second order in epsilon. Using a conjecture we extend the calculation to 11th order and discuss the convergence of the resulting series

First order phase transition in a nonequilibrium growth process

We introduce a simple continuous model for nonequilibrium surface growth. The dynamics of the system is defined by the KPZ equation with a Morse-like potential representing a short range interaction between the surface and the substrate. The mean field solution displays a non trivial phase diagram with a first order transition between a growing and a bound surface, associated with a region of coexisting phases, and a tricritical point where the transition becomes second order. Numerical simulations in 3 dimensions show quantitative agreement with mean field results, and the features of the phase space are preserved even in 2 dimensions.Comment: 7 figures, revtex, submitted to Phys. Rev.

Strong anisotropy in two-dimensional surfaces with generic scale invariance: Gaussian and related models

Among systems that display generic scale invariance, those whose asymptotic properties are anisotropic in space (strong anisotropy, SA) have received a relatively smaller attention, specially in the context of kinetic roughening for two-dimensional surfaces. This is in contrast with their experimental ubiquity, e.g. in the context of thin film production by diverse techniques. Based on exact results for integrable (linear) cases, here we formulate a SA Ansatz that, albeit equivalent to existing ones borrowed from equilibrium critical phenomena, is more naturally adapted to the type of observables that are measured in experiments on the dynamics of thin films, such as one and two-dimensional height structure factors. We test our Ansatz on a paradigmatic nonlinear stochastic equation displaying strong anisotropy like the Hwa-Kardar equation [Phys. Rev. Lett. 62, 1813 (1989)], that was initially proposed to describe the interface dynamics of running sand piles. A very important role to elucidate its SA properties is played by an accurate (Gaussian) approximation through a non-local linear equation that shares the same asymptotic properties

Sum of exit times in series of metastable states in probabilistic cellular automata

Reversible Probabilistic Cellular Automata are a special class of automata whose stationary behavior is described by Gibbs--like measures. For those models the dynamics can be trapped for a very long time in states which are very different from the ones typical of stationarity. This phenomenon can be recasted in the framework of metastability theory which is typical of Statistical Mechanics. In this paper we consider a model presenting two not degenerate in energy metastable states which form a series, in the sense that, when the dynamics is started at one of them, before reaching stationarity, the system must necessarily visit the second one. We discuss a rule for combining the exit times from each of the metastable states

Global visualization and quantification of compressible vortex loops

The physics of compressible vortex loops generated due to the rolling up of the shear layer upon the diffraction of a shock wave from a shock tube is far from being understood, especially when shock-vortex interactions are involved. This is mainly due to the lack of global quantitative data available which characterizes the flow. The present study involves the usage of the PIV technique to characterize the velocity and vorticity of compressible vortex loops formed at incident shock Mach numbers ofM=1.54 and1.66. Another perk of the PIV technique over purely qualitative methods, which has been demonstrated in the current study, is that at the same time the results also provide a clear image of the various flow features. Techniques such as schlieren and shadowgraph rely on density gradients present in the flow and fail to capture regions of the flow influenced by the primary flow structure which would have relatively lower pressure and density. Various vortex loops, namely, square, elliptic and circular, were generated using different shape adaptors fitted to the end of the shock tube. The formation of a coaxial vortex loop with opposite circulation along with the generation of a third stronger vortex loop ahead of the primary with same circulation direction are of the interesting findings of the current study

Bc spectroscopy in a quantum-chromodynamic potential model

We have investigated $B_c$ spectroscopy with the use of a quantum-chromodynamic potential model which was recently used by us for the light-heavy quarkonia. We give our predictions for the energy levels and the $E$1 transition widths. We also find, rather surprisingly, that although $B_c$ is not a light-heavy system, the heavy quark effective theory with the inclusion of the $m_b^{-1}$ and $m_b^{-1}\ln m_b$ corrections is as successful for $B_c$ as it is for $B$ and $B_s$.Comment: 10 page ReVTeX pape