Jets or vortices - what flows are generated by an inverse turbulent cascade?

An inverse cascade{energy transfer to progressively larger scales{is a salient feature of two-dimensional turbulence. If the cascade reaches the system scale, it creates a coherent ow expected to have the largest available scale and conform with the symmetries of the domain. In a doubly periodic rectangle, the mean ow with zero total momentum was therefore believed to be unidirec- tional, with two jets along the short side; while for an aspect ratio close to unity, a vortex dipole was expected. Using direct numerical simulations, we show that in fact neither the box symmetry is respected nor the largest scale is realized: the ow is never purely unidirectional since the inverse cascade produces coherent vortices, whose number and relative motion are determined by the aspect ratio. This spontaneous symmetry breaking is closely related to the hierarchy of averaging times. Long-time averaging restores translational invariance due to vortex wandering along one direction, and gives jets whose profile, however, can be deduced neither from the largest-available-scale argument, nor from the often employed maximum-entropy principle or quasilinear approximation

A numerical study of the RG equation for the deformed O(3)O(3) nonlinear sigma model

The Renormalization Group equation describing the evolution of the metric of the nonlinear sigma model poses some nice mathematical problems involving functional analysis, differential geometry and numerical analysis. In this article we briefly report some results obtained from the numerical study of the solutions in the case of a two dimensional target space (deformation of the $O(3)$ sigma model). In particular, our analysis shows that the so-called sausages define an attracting manifold in the $U(1)$-symmetric case, at one-loop level. Moreover, data from two-loop evolution are used to test the association put forward in Nucl. Phys., B406 (1993) 521 between the so-called $SSM_{\nu}$ field theory and a certain $U(1)$-symmetric, factorized scattering theory (FST).Comment: LaTex (RevTex style), 16 pages, 6 uuencoded figures. Minor technical changes

Axial anomaly: the modern status

The modern status of the problem of axial anomaly in QED and QCD is reviewed. Two methods of the derivation of the axial anomaly are presented: 1) by splitting of coordinates in the expression for the axial current and 2) by calculation of triangle diagrams, where the anomaly arises from the surface terms in momentum space. It is demonstrated, that the equivalent formulation of the anomaly can be given, as a sum rule for the structure function in dispersion representation of three point function of AVV interaction. It is argued, that such integral representation of the anomaly has some advantages in the case of description of the anomaly by contribution of hadronic states in QCD. The validity of the t'Hooft consistency condition is discussed. Few examples of the physical application of the axial anomaly are given.Comment: 17 pages, 3 figures, to be published in International Journal of Modern Physics A, few minor correction were done, two references were adde

Anomalies without Massless Particles

Baryon and lepton number in the standard model are violated by anomalies, even though the fermions are massive. This problem is studied in the context of a two dimensional model. In a uniform background field, fermion production arise from non-adiabatic behavior that compensates for the absence of massless modes. On the other hand, for localized instanton-like configurations, there is an adiabatic limit. In this case, the anomaly is produced by bound states which travel across the mass gap. The sphaleron corresponds to a bound state at the halfway point.Comment: (26 pages, 3 figures, uses harvmac and uufiles), UCSD/PTH 93-3

Resonant Tunneling through Linear Arrays of Quantum Dots

We theoretically investigate resonant tunneling through a linear array of quantum dots with subsequent tunnel coupling. We consider two limiting cases: (i) strong Coulomb blockade, where only one extra electron can be present in the array (ii) limit of almost non-interacting electrons. We develop a density matrix description that incorporates the coupling of the dots to reservoirs. We analyze in detail the dependence of the stationary current on the electron energies, tunnel matrix elements and rates, and on the number of dots. We describe interaction and localization effects on the resonant current. We analyze the applicability of the approximation of independent conduction channels. We find that this approximation is not valid when at least one of the tunnel rates to the leads is comparable to the energy splitting of the states in the array. In this case the interference of conduction processes through different channels suppresses the current.Comment: 12 pages, 5 figure

Holographic two dimensional QCD and Chern-Simons term

We present a holographic realization of large Nc massless QCD in two dimensions using a D2/D8 brane construction. The flavor axial anomaly is dual to a three dimensional Chern-Simons term which turns out to be of leading order, and it affects the meson spectrum and holographic renormalization in crucial ways. The massless flavor bosons that exist in the spectrum are found to decouple from the heavier mesons, in agreement with the general lore of non-Abelian bosonization. We also show that an external dynamical photon acquires a mass through the three dimensional Chern-Simons term as expected from the Schwinger mechanism. Massless two dimensional QCD at large Nc exhibits anti-vector-meson dominance due to the axial anomaly.Comment: 22 page

Higher algebras and mesonic spectrum in two-dimensional QCD

We construct composite operators in two-dimensional bosonized QCD, which obey a $W_\infty$ algebra, and discuss their relation to analogous objects recently obtained in the fermionic language. A complex algebraic structure is unravelled, supporting the idea that the model is integrable. For singlets we find a mass spectrum obeying the Regge behavior.Comment: 11 pages, plain tex, prep. CERN-TH 7365/94, July 199

Disorder Effects in Two-Dimensional d-wave Superconductors

Influence of weak nonmagnetic impurities on the single-particle density of states $\rho(\omega)$ of two-dimensional electron systems with a conical spectrum is studied. We use a nonperturbative approach, based on replica trick with subsequent mapping of the effective action onto a one-dimensional model of interacting fermions, the latter being treated by Abelian and non-Abelian bosonization methods. It is shown that, in a d-wave superconductor, the density of states, averaged over randomness, follows a nontrivial power-law behavior near the Fermi energy: $\rho(\omega) \sim |\omega|^{\alpha}$. The exponent $\alpha>0$ is calculated for several types of disorder. We demonstrate that the property $\rho(0) = 0$ is a direct consequence of a {\it continuous} symmetry of the effective fermionic model, whose breakdown is forbidden in two dimensions. As a counter example, we consider another model with a conical spectrum - a two-dimensional orbital antiferromagnet, where static disorder leads to a finite $\rho(0)$ due to breakdown of a {\it discrete} (particle-hole) symmetry.Comment: 24 pages, 3 figures upon request, RevTe

About the realization of chiral symmetry in QCD2

Two dimensional massless Quantum Chromodynamics presents many features which resemble those of the true theory. In particular the spectrum consists of mesons and baryons arranged in flavor multiplets without parity doubling. We analyze the implications of chiral symmetry, which is not spontaneously broken in two dimensions, in the spectrum and in the quark condensate. We study how parity doubling, an awaited consequence of Coleman's theorem, is avoided due to the dimensionality of space-time and confinement. We prove that a chiral phase transition is not possible in the theory.Comment: 9 pages, latex, ftuv/92-

Effective Lagrangians in 2+ϵ2 + \epsilon Dimensions

The failure of the the loop expansion and effective lagrangians in two dimensions, which traditionally hinges on a power counting argument is considered. We establish that the book keeping device for the loop expansion, a role played by (the reciprocal of) the pion-decay constant itself vanishes for $d=2$, thereby going beyond the power counting argument. We point the connection of our results to the distinct phases of the candidate for the effective lagrangians, the non-linear sigma model, in $d=2+\epsilon$, and eventually for $d=2$. In light of our results, we recall some of the relavant features of the multi-flavor Schwinger and large $N_f$ $QCD_2$ as candidates for the underlying theory in $d=2$.Comment: 13 pages plain LaTeX, to be run twice. Replaced with expanded and corrected version. One footnote adde