Langevin Simulation of the Chirally Decomposed Sine-Gordon Model

A large class of quantum and statistical field theoretical models, encompassing relevant condensed matter and non-abelian gauge systems, are defined in terms of complex actions. As the ordinary Monte-Carlo methods are useless in dealing with these models, alternative computational strategies have been proposed along the years. The Langevin technique, in particular, is known to be frequently plagued with difficulties such as strong numerical instabilities or subtle ergodic behavior. Regarding the chirally decomposed version of the sine-Gordon model as a prototypical case for the failure of the Langevin approach, we devise a truncation prescription in the stochastic differential equations which yields numerical stability and is assumed not to spoil the Berezinskii-Kosterlitz-Thouless transition. This conjecture is supported by a finite size scaling analysis, whereby a massive phase ending at a line of critical points is clearly observed for the truncated stochastic model.Comment: 6 pages, 4 figure

The SO(N) principal chiral field on a half-line

We investigate the integrability of the SO(N) principal chiral model on a half-line, and find that mixed Dirichlet/Neumann boundary conditions (as well as pure Dirichlet or Neumann) lead to infinitely many conserved charges classically in involution. We use an anomaly-counting method to show that at least one non-trivial example survives quantization, compare our results with the proposed reflection matrices, and, based on these, make some preliminary remarks about expected boundary bound-states.Comment: 7 pages, Late

Supersymmetric WZW σ\sigma Model on Full and Half Plane

We study classical integrability of the supersymmetric U(N) $\sigma$ model with the Wess-Zumino-Witten term on full and half plane. We demonstrate the existence of nonlocal conserved currents of the model and derive general recursion relations for the infinite number of the corresponding charges in a superfield framework. The explicit form of the first few supersymmetric charges are constructed. We show that the considered model is integrable on full plane as a concequence of the conservation of the supersymmetric charges. Also, we study the model on half plane with free boundary, and examine the conservation of the supersymmetric charges on half plane and find that they are conserved as a result of the equations of motion and the free boundary condition. As a result, the model on half plane with free boundary is integrable. Finally, we conclude the paper and some features and comments are presented.Comment: 12 pages. submitted to IJMP

Special Theory of Relativity through the Doppler Effect

We present the special theory of relativity taking the Doppler effect as the starting point, and derive several of its main effects, such as time dilation, length contraction, addition of velocities, and the mass-energy relation, and assuming energy and momentum conservation, we discuss how to introduce the 4-momentum in a natural way. We also use the Doppler effect to explain the "twin paradox", and its version on a cylinder. As a by-product we discuss Bell's spaceship paradox, and the Lorentz transformation for arbitrary velocities in one dimension.Comment: 20 pages, 1 figur

On the Beta Function for Anisotropic Current Interactions in 2D

By making use of current-algebra Ward identities we study renormalization of general anisotropic current-current interactions in 2D. We obtain a set of algebraic conditions that ensure the renormalizability of the theory to all orders. In a certain minimal prescription we compute the beta function to all orders.Comment: 7 pages, 6 figures. v2: References added and typos corrected; v3: cancellation of finite parts more accurately state

Log-Poisson Cascade Description of Turbulent Velocity Gradient Statistics

The Log-Poisson phenomenological description of the turbulent energy cascade is evoked to discuss high-order statistics of velocity derivatives and the mapping between their probability distribution functions at different Reynolds numbers. The striking confirmation of theoretical predictions suggests that numerical solutions of the flow, obtained at low/moderate Reynolds numbers can play an important quantitative role in the analysis of experimental high Reynolds number phenomena, where small scales fluctuations are in general inaccessible from direct numerical simulations

Large Abundances of Polycyclic Aromatic Hydrocarbons in Titan's Upper Atmosphere

In this paper, we analyze the strong unidentified emission near 3.28 micron in Titan's upper daytime atmosphere recently discovered by Dinelli et al.We have studied it by using the NASA Ames PAH IR Spectroscopic Database. The polycyclic aromatic hydrocarbons (PAHs), after absorbing UV solar radiation, are able to emit strongly near 3.3 micron. By using current models for the redistribution of the absorbed UV energy, we have explained the observed spectral feature and have derived the vertical distribution of PAH abundances in Titan's upper atmosphere. PAHs have been found to be present in large concentrations, about (2-3) 10(exp 4) particles / cubic cm. The identified PAHs have 9-96 carbons, with a concentration-weighted average of 34 carbons. The mean mass is approx 430 u; the mean area is about 0.53 sq. nm; they are formed by 10-11 rings on average, and about one-third of them contain nitrogen atoms. Recently, benzene together with light aromatic species as well as small concentrations of heavy positive and negative ions have been detected in Titan's upper atmosphere. We suggest that the large concentrations of PAHs found here are the neutral counterpart of those positive and negative ions, which hence supports the theory that the origin of Titan main haze layer is located in the upper atmosphere

Beyond scaling and locality in turbulence

An analytic perturbation theory is suggested in order to find finite-size corrections to the scaling power laws. In the frame of this theory it is shown that the first order finite-size correction to the scaling power laws has following form $S(r) \cong cr^{\alpha_0}[\ln(r/\eta)]^{\alpha_1}$, where $\eta$ is a finite-size scale (in particular for turbulence, it can be the Kolmogorov dissipation scale). Using data of laboratory experiments and numerical simulations it is shown shown that a degenerate case with $\alpha_0 =0$ can describe turbulence statistics in the near-dissipation range $r > \eta$, where the ordinary (power-law) scaling does not apply. For moderate Reynolds numbers the degenerate scaling range covers almost the entire range of scales of velocity structure functions (the log-corrections apply to finite Reynolds number). Interplay between local and non-local regimes has been considered as a possible hydrodynamic mechanism providing the basis for the degenerate scaling of structure functions and extended self-similarity. These results have been also expanded on passive scalar mixing in turbulence. Overlapping phenomenon between local and non-local regimes and a relation between position of maximum of the generalized energy input rate and the actual crossover scale between these regimes are briefly discussed.Comment: extended versio

Circulation Statistics in Three-Dimensional Turbulent Flows

We study the large $\lambda$ limit of the loop-dependent characteristic functional $Z(\lambda)=$, related to the probability density function (PDF) of the circulation around a closed contour $c$. The analysis is carried out in the framework of the Martin-Siggia-Rose field theory formulation of the turbulence problem, by means of the saddle-point technique. Axisymmetric instantons, labelled by the component $\sigma_{zz}$ of the strain field -- a partially annealed variable in our formalism -- are obtained for a circular loop in the $xy$ plane, with radius defined in the inertial range. Fluctuations of the velocity field around the saddle-point solutions are relevant, leading to the lorentzian asymptotic behavior $Z(\lambda) \sim 1/{\lambda^2}$. The ${\cal O}(1 / {\lambda^4})$ subleading correction and the asymmetry between right and left PDF tails due to parity breaking mechanisms are also investigated.Comment: Computations are discussed in a more detailed way; accepted for publication in Physical Review

Effective action for QED in 2+1 dimensions at finite temperature

We calculate the effective action for a constant magnetic field and a time-dependent time-component of the gauge field in 2+1 dimensions at finite temperature. We also discuss the behaviour of the charge density and the fermion condensate as order parameters of symmetry breaking.Comment: Latex, 10 pages, no figure