Classical Time Crystals

We consider the possibility that classical dynamical systems display motion in their lowest energy state, forming a time analogue of crystalline spatial order. Challenges facing that idea are identified and overcome. We display arbitrary orbits of an angular variable as lowest-energy trajectories for nonsingular Lagrangian systems. Dynamics within orbits of broken symmetry provide a natural arena for formation of time crystals. We exhibit models of that kind, including a model with traveling density waves.Comment: 5 pages, 1 figur

Anyonic Realization of the Quantum Affine Lie Algebra U_q(A_N)

We give a realization of quantum affine Lie algebra $U_q(\hat A_{N-1})$ in terms of anyons defined on a two-dimensional lattice, the deformation parameter $q$ being related to the statistical parameter $\nu$ of the anyons by $q = e^{i\pi\nu}$. In the limit of the deformation parameter going to one we recover the Feingold-Frenkel fermionic construction of undeformed affine Lie algebra.Comment: 13p LaTeX Document (should be run twice

Free Relativistic Anyons with Canonical Spin Algebra

We discuss a relativistic free particle with fractional spin in 2+1 dimensions, where the dual spin components satisfy the canonical angular momentum algebra $\left\{ S_\mu , S_\nu \right\}\,=\,\epsilon_{\mu \nu \gamma}S^\gamma$. It is shown that it is a general consequence of these features that the Poincar\`e invariance is broken down to the Lorentz one, so indicating that it is not possible to keep simultaneously the free nature of the anyon and the translational invariance.Comment: Complete version with reference

A Simple Action for a Free Anyon

By studying classical realizations of the sl(2,R) algebra in a two dimensional phase space $(q,\pi)$, we have derived a continuous family of new actions for free anyons in 2+1 dimensions. For the case of light-like spin vector $(S_\mu S^\mu =0)$, the action is remarkably simple. We show the appearence of the Zitterbewegung in the solutions of the equations of motion, and relate the actions to others in the literature at classical level.Comment: 15 pages, Plain Late

Is there an attraction between spinons in the Haldane--Shastry model?

While the Bethe Ansatz solution of the Haldane--Shastry model appears to suggest that the spinons represent a free gas of half-fermions, Bernevig, Giuliano, and Laughlin (BGL) (cond-mat/0011069, cond-mat/0011270) have concluded recently that there is an attractive interaction between spinons. We argue that the dressed scattering matrix obtained with the asymptotic Bethe Ansatz is to be interpreted as the true and physical scattering matrix of the excitations, and hence, that the result by BGL is inconsistent with an earlier result by Essler (cond-mat/9406081). We critically re-examine the analysis of BGL, and conclude that there is no interaction between spinons or spinons and holons in the Haldane--Shastry model

Theory for the single-point velocity statistics of fully developed turbulence

We investigate the single-point velocity probability density function (PDF) in three-dimensional fully developed homogeneous isotropic turbulence within the framework of PDF equations focussing on deviations from Gaussianity. A joint analytical and numerical analysis shows that these deviations may be quantified studying correlations of dynamical quantities like pressure gradient, external forcing and energy dissipation with the velocity. A stationary solution for the PDF equation in terms of these quantities is presented, and the theory is validated with the help of direct numerical simulations indicating sub-Gaussian tails of the PDF.Comment: 6 pages, 4 figures, corrected typo in eq. (4

The Lundgren-Monin-Novikov Hierarchy: Kinetic Equations for Turbulence

We present an overview of recent works on the statistical description of turbulent flows in terms of probability density functions (PDFs) in the framework of the Lundgren-Monin-Novikov (LMN) hierarchy. Within this framework, evolution equations for the PDFs are derived from the basic equations of fluid motion. The closure problem arises either in terms of a coupling to multi-point PDFs or in terms of conditional averages entering the evolution equations as unknown functions. We mainly focus on the latter case and use data from direct numerical simulations (DNS) to specify the unclosed terms. Apart from giving an introduction into the basic analytical techniques, applications to two-dimensional vorticity statistics, to the single-point velocity and vorticity statistics of three-dimensional turbulence, to the temperature statistics of Rayleigh-B\'enard convection and to Burgers turbulence are discussed.Comment: Accepted for publication in C. R. Acad. Sc

A Model of Comprehensive Unification

Comprehensive - that is, gauge and family - unification using spinors has many attractive features, but it has been challenged to explain chirality. Here, by combining an orbifold construction with more traditional ideas, we address that difficulty. Our candidate model features three chiral families and leads to an acceptable result for quantitative unification of couplings. A potential target for accelerator and astronomical searches emerges.Comment: 5 pages, 2 figures. Published versio

Modeling space-time correlations of velocity fluctuations in wind farms

An analytical model for the streamwise velocity space-time correlations in turbulent flows is derived and applied to the special case of velocity fluctuations in large wind farms. The model is based on the Kraichnan-Tennekes random sweeping hypothesis, capturing the decorrelation in time while including a mean wind velocity in the streamwise direction. In the resulting model, the streamwise velocity space-time correlation is expressed as a convolution of the pure space correlation with an analytical temporal decorrelation kernel. Hence, the spatio-temporal structure of velocity fluctuations in wind farms can be derived from the spatial correlations only. We then explore the applicability of the model to predict spatio-temporal correlations in turbulent flows in wind farms. Comparisons of the model with data from a large eddy simulation of flow in a large, spatially periodic wind farm are performed, where needed model parameters such as spatial and temporal integral scales and spatial correlations are determined from the large eddy simulation. Good agreement is obtained between the model and large eddy simulation data showing that spatial data may be used to model the full temporal structure of fluctuations in wind farms.Comment: Submitted to Wind Energ

Parity Violation in Aharonov-Bohm Systems: The Spontaneous Hall Effect

We show how macroscopic manifestations of $P$ (and $T$) symmetry breaking can arise in a simple system subject to Aharonov-Bohm interactions. Specifically, we study the conductivity of a gas of charged particles moving through a dilute array of flux tubes. The interaction of the electrons with the flux tubes is taken to be of a purely Aharonov-Bohm type. We find that the system exhibits a non-zero transverse conductivity, i.e., a spontaneous Hall effect. This is in contrast with the fact that the cross sections for both scattering and bremsstrahlung (soft photon emission) of a single electron from a flux tube are invariant under reflections. We argue that the asymmetry in the conductivity coefficients arises from many-body effects. On the other hand, the transverse conductivity has the same dependence on universal constants that appears in the Quantum Hall Effect, a result that we relate to the validity of the Mean Field approximation.Comment: 12 pages (4 figures available upon request), RevTex, EHU-FT-93/1