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

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

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

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

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

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

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

Vacuum Energy: Myths and Reality

We discuss the main myths related to the vacuum energy and cosmological constant, such as: ``unbearable lightness of space-time''; the dominating contribution of zero point energy of quantum fields to the vacuum energy; non-zero vacuum energy of the false vacuum; dependence of the vacuum energy on the overall shift of energy; the absolute value of energy only has significance for gravity; the vacuum energy depends on the vacuum content; cosmological constant changes after the phase transition; zero-point energy of the vacuum between the plates in Casimir effect must gravitate, that is why the zero-point energy in the vacuum outside the plates must also gravitate; etc. All these and some other conjectures appear to be wrong when one considers the thermodynamics of the ground state of the quantum many-body system, which mimics macroscopic thermodynamics of quantum vacuum. In particular, in spite of the ultraviolet divergence of the zero-point energy, the natural value of the vacuum energy is comparable with the observed dark energy. That is why the vacuum energy is the plausible candidate for the dark energy.Comment: 24 pages, 2 figures, submitted to the special issue of Int. J. Mod. Phys. devoted to dark energy and dark matter, IJMP styl

Relevance of multiple-quasiparticle tunneling between edge states at \nu =p/(2np+1)

We present an explanation for the anomalous behavior in tunneling conductance and noise through a point contact between edge states in the Jain series $\nu=p/(2np+1)$, for extremely weak-backscattering and low temperatures [Y.C. Chung, M. Heiblum, and V. Umansky, Phys. Rev. Lett. {\bf{91}}, 216804 (2003)]. We consider edge states with neutral modes propagating at finite velocity, and we show that the activation of their dynamics causes the unexpected change in the temperature power-law of the conductance. Even more importantly, we demonstrate that multiple-quasiparticles tunneling at low energies becomes the most relevant process. This result will be used to explain the experimental data on current noise where tunneling particles have a charge that can reach $p$ times the single quasiparticle charge. In this paper we analyze the conductance and the shot noise to substantiate quantitatively the proposed scenario.Comment: 4 pages, 2 figure

Quantum Numbers of Textured Hall Effect Quasiparticles

We propose a class of variational wave functions with slow variation in spin and charge density and simple vortex structure at infinity, which properly generalize both the Laughlin quasiparticles and baby Skyrmions. We argue that the spin of the corresponding quasiparticle has a fractional part related in a universal fashion to the properties of the bulk state, and propose a direct experimental test of this claim. We show that certain spin-singlet quantum Hall states can be understood as arising from primary polarized states by Skyrmion condensation.Comment: 13 pages, no figures, Phyzz