About coherent structures in random shell models for passive scalar advection

A study of anomalous scaling in models of passive scalar advection in terms of singular coherent structures is proposed. The stochastic dynamical system considered is a shell model reformulation of Kraichnan model. We extend the method introduced in \cite{DDG99} to the calculation of self-similar instantons and we show how such objects, being the most singular events, are appropriate to capture asymptotic scaling properties of the scalar field. Preliminary results concerning the statistical weight of fluctuations around these optimal configurations are also presented.Comment: 4 pages, 2 postscript figures, submitted to PR

Phases of the 2D Hubbard model at low doping

We show that the planar spiral phase of the 2D Hubbard model at low doping, x, is unstable towards a noncoplanar spin configuration. The novel equilibrium state we found at low doping is incommensurate with the inverse pitch of the spiral varying as x^(1/2), but nevertheless has a dominant peak in the susceptibility at (\pi,\pi). Relevance to the NMR and neutron scattering experiments in La_2-xSr_xCuO_4 is disccussed.Comment: 12 pages, emtex v.3.

Computation of the radiation amplitude of oscillons

The radiation loss of small amplitude oscillons (very long-living, spatially localized, time dependent solutions) in one dimensional scalar field theories is computed in the small-amplitude expansion analytically using matched asymptotic series expansions and Borel summation. The amplitude of the radiation is beyond all orders in perturbation theory and the method used has been developed by Segur and Kruskal in Phys. Rev. Lett. 58, 747 (1987). Our results are in good agreement with those of long time numerical simulations of oscillons.Comment: 22 pages, 9 figure

Outliers, Extreme Events and Multiscaling

Extreme events have an important role which is sometime catastrophic in a variety of natural phenomena including climate, earthquakes and turbulence, as well as in man-made environments like financial markets. Statistical analysis and predictions in such systems are complicated by the fact that on the one hand extreme events may appear as "outliers" whose statistical properties do not seem to conform with the bulk of the data, and on the other hands they dominate the (fat) tails of probability distributions and the scaling of high moments, leading to "abnormal" or "multi"-scaling. We employ a shell model of turbulence to show that it is very useful to examine in detail the dynamics of onset and demise of extreme events. Doing so may reveal dynamical scaling properties of the extreme events that are characteristic to them, and not shared by the bulk of the fluctuations. As the extreme events dominate the tails of the distribution functions, knowledge of their dynamical scaling properties can be turned into a prediction of the functional form of the tails. We show that from the analysis of relatively short time horizons (in which the extreme events appear as outliers) we can predict the tails of the probability distribution functions, in agreement with data collected in very much longer time horizons. The conclusion is that events that may appear unpredictable on relatively short time horizons are actually a consistent part of a multiscaling statistics on longer time horizons.Comment: 11 pages, 14 figures included, PRE submitte

Polarization of superfluid turbulence

We show that normal fluid eddies in turbulent helium II polarize the tangle of quantized vortex lines present in the flow, thus inducing superfluid vorticity patterns similar to the driving normal fluid eddies. We also show that the polarization is effective over the entire inertial range. The results help explain the surprising analogies between classical and superfluid turbulence which have been observed recently.Comment: 3 figure

Superconducting Spiral Phase in the two-dimensional t-J model

We analyse the t-t'-t''-J model, relevant to the superconducting cuprates. By using chiral perturbation theory we have determined the ground state to be a spiral for small doping \delta << 1 near half filling. In this limit the solution does not contain any uncontrolled approximations. We evaluate the spin-wave Green's functions and address the issue of stability of the spiral state, leading to the phase diagram of the model. At t'=t''=0 the spiral state is unstable towards a local enhancement of the spiral pitch, and the nature of the true ground state remains unclear. However, for values of t' and t'' corresponding to real cuprates the (1,0) spiral state is stabilized by quantum fluctuations (``order from disorder'' effect). We show that at \delta = 0.119 the spiral is commensurate with the lattice with a period of 8 lattice spacings. It is also demonstrated that spin-wave mediated superconductivity develops in the spiral state and a lower limit for the superconducting gap is derived. Even though one cannot classify the gap symmetry according to the lattice representations (s,p,d,...) since the symmetry of the lattice is spontaneously broken by the spiral, the gap always has lines of nodes along the (1,\pm 1) directions.Comment: 17 pages, 11 figure

Pulses in the Zero-Spacing Limit of the GOY Model

We study the propagation of localised disturbances in a turbulent, but momentarily quiescent and unforced shell model (an approximation of the Navier-Stokes equations on a set of exponentially spaced momentum shells). These disturbances represent bursts of turbulence travelling down the inertial range, which is thought to be responsible for the intermittency observed in turbulence. Starting from the GOY shell model, we go to the limit where the distance between succeeding shells approaches zero (``the zero spacing limit'') and helicity conservation is retained. We obtain a discrete field theory which is numerically shown to have pulse solutions travelling with constant speed and with unchanged form. We give numerical evidence that the model might even be exactly integrable, although the continuum limit seems to be singular and the pulses show an unusual super exponential decay to zero as $\exp(- \mathrm{const} \sigma^n)$ when $n \to \infty$, where $\sigma$ is the {\em golden mean}. For finite momentum shell spacing, we argue that the pulses should accelerate, moving to infinity in a finite time. Finally we show that the maximal Lyapunov exponent of the GOY model approaches zero in this limit.Comment: 27 pages, submitted for publicatio

A hidden Goldstone mechanism in the Kagom\'e lattice antiferromagnet

In this paper, we study the phases of the Heisenberg model on the \kagome lattice with antiferromagnetic nearest neighbour coupling $J_1$ and ferromagnetic next neighbour coupling $J_2$. Analysing the long wavelength, low energy effective action that describes this model, we arrive at the phase diagram as a function of $\chi = \frac{J_2}{J_1}$. The interesting part of this phase diagram is that for small $\chi$, which includes $\chi =0$, there is a phase with no long range spin order and with gapless and spin zero low lying excitations. We discuss our results in the context of earlier, numerical and experimental work.Comment: 21 pages, latex file with 5 figure