Temperature Dependence of Gluon and Quark Condensates as from Linear Confinement

The gluon and quark condensates and their temperature dependence are investigated within QCD premises. The input for the former is a gauge invariant $gg$ kernel made up of the direct (D), exchange (X) and contact(C) QCD interactions in the lowest order, but with the perturbative propagator $k^{-2}$ replaced by a `non-perturbative $k^{-4}$ form obtained via two differentiations: $\mu^2 \partial_m^2 (m^2+k^2)^{-1}$, ($\mu$ a scale parameter), and then setting $m=0$, to simulate linear confinement. Similarly for the input $q{\bar q}$ kernel the gluon propagator is replaced by the above $k^{-4}$ form. With these `linear' simulations, the respective condensates are obtained by `looping' up the gluon and quark lines in the standard manner. Using Dimensional regularization (DR), the necessary integrals yield the condensates plus temperature corrections, with a common scale parameter $\mu$ for both. For gluons the exact result is $$= {36\mu^4}\pi^{-3}\alpha_s(\mu^2)[2-\gamma - 4\pi^2 T^2/(3\mu^2)]$$. Evaluation of the quark condensate is preceded by an approximate solution of the SDE for the mass function $m(p)$, giving a recursive formula, with convergence achieved at the third iteration. Setting the scale parameter $\mu$ equal to the universal Regge slope $1 GeV^2$, the gluon and quark condensates at T=0 are found to be $0.586 Gev^4$ and $(240-260 MeV)^3$ respectively, in fair accord with QCD sum rule values. Next, the temperature corrections (of order $-T^2$ for both condensates) is determined via finite-temperature field theory a la Matsubara. Keywords: Gluon Condensate, mass tensor, gauge invariance, linear confinement, finite-temperature, contour-closing. PACS: 11.15.Tk ; 12.38.Lg ; 13.20.CzComment: 13 pages (LaTeX) including 2 figure

Baryon Self-Energy With QQQ Bethe-Salpeter Dynamics In The Non-Perturbative QCD Regime: n-p Mass Difference

A qqq BSE formalism based on DB{\chi}S of an input 4-fermion Lagrangian of `current' u,d quarks interacting pairwise via gluon-exchange-propagator in its {\it non-perturbative} regime, is employed for the calculation of baryon self-energy via quark-loop integrals. To that end the baryon-qqq vertex function is derived under Covariant Instantaneity Ansatz (CIA), using Green's function techniques. This is a 3-body extension of an earlier q{\bar q} (2-body) result on the exact 3D-4D interconnection for the respective BS wave functions under 3D kernel support, precalibrated to both q{\bar q} and qqq spectra plus other observables. The quark loop integrals for the neutron (n) - proton (p) mass difference receive contributions from : i) the strong SU(2) effect arising from the d-u mass difference (4 MeV); ii) the e.m. effect of the respective quark charges. The resultant n-p difference comes dominantly from d-u effect (+1.71 Mev), which is mildly offset by e.m.effect (-0.44), subject to gauge corrections. To that end, a general method for QED gauge corrections to an arbitrary momentum dependent vertex function is outlined, and on on a proportionate basis from the (two-body) kaon case, the net n-p difference works out at just above 1 MeV. A critical comparison is given with QCD sum rules results.Comment: be 27 pages, Latex file, and to be published in IJMPA, Vol 1

Experimental Quantification of Entanglement Through Heat Capacity

A new experimental realization of heat capacity as an entanglement witness (EW) is reported. Entanglement properties of a low dimensional quantum spin system are investigated by heat capacity measurements performed down to very low temperatures (400mK), for various applied magnetic field values. The experimentally extracted results for the value of heat capacity at zero field matches perfectly with the theoretical estimates of entanglement from model Hamiltonians. The studied sample is a spin $\frac{1}{2}$ antiferromagnetic system which shows clear signature of quantum phase transition (QPT) at very low temperatures when the heat capacity is varied as a function of fields at a fixed temperature. The variation of entanglement as a function of field is then explored in the vicinity of the quantum phase transition to capture the sudden loss of entanglement.Comment: 8 pages, 6 figures, To be published in NJ

Metrics for comparing neuronal tree shapes based on persistent homology

As more and more neuroanatomical data are made available through efforts such as NeuroMorpho.Org and FlyCircuit.org, the need to develop computational tools to facilitate automatic knowledge discovery from such large datasets becomes more urgent. One fundamental question is how best to compare neuron structures, for instance to organize and classify large collection of neurons. We aim to develop a flexible yet powerful framework to support comparison and classification of large collection of neuron structures efficiently. Specifically we propose to use a topological persistence-based feature vectorization framework. Existing methods to vectorize a neuron (i.e, convert a neuron to a feature vector so as to support efficient comparison and/or searching) typically rely on statistics or summaries of morphometric information, such as the average or maximum local torque angle or partition asymmetry. These simple summaries have limited power in encoding global tree structures. Based on the concept of topological persistence recently developed in the field of computational topology, we vectorize each neuron structure into a simple yet informative summary. In particular, each type of information of interest can be represented as a descriptor function defined on the neuron tree, which is then mapped to a simple persistence-signature. Our framework can encode both local and global tree structure, as well as other information of interest (electrophysiological or dynamical measures), by considering multiple descriptor functions on the neuron. The resulting persistence-based signature is potentially more informative than simple statistical summaries (such as average/mean/max) of morphometric quantities-Indeed, we show that using a certain descriptor function will give a persistence-based signature containing strictly more information than the classical Sholl analysis. At the same time, our framework retains the efficiency associated with treating neurons as points in a simple Euclidean feature space, which would be important for constructing efficient searching or indexing structures over them. We present preliminary experimental results to demonstrate the effectiveness of our persistence-based neuronal feature vectorization framework

The Geometry of PSR B0031-07

PSR B0031-07 is well known to exhibit three different modes of drifting sub-pulses (mode A, B and C). It has recently been shown that in a multifrequency observation, consisting of 2700 pulses, all driftmodes were visible at low frequencies, while at 4.85 GHz only mode-A drift or non-drifting emission was detected. This suggests that modes A and B are emitted in sub-beams, rotating at a fixed distance from the magnetic axis, with the mode-B sub-beams being closer to the magnetic axis than the mode-A sub-beams. Diffuse emission between the sub-beams can account for the non-drifting emission. Using the results of an analysis of simultaneous multifrequency observations of PSR B0031-07, we set out to construct a geometrical model that includes emission from both sub-beams and diffuse emission and describes the regions of the radio emission of PSR B0031-07 at each emission frequency for driftmodes A and B. Based on the vertical spacing between driftbands, we have determined the driftmode of each sequence of drift. To restrict the model, we calculated average polarisation and intensity characteristics for each driftmode and at each frequency. The model reproduces the observed polarisation and intensity characteristics, suggesting that diffuse emission plays an important role in the emission properties of PSR B0031-07. The model further suggests that the emission heights of this pulsar range from a few kilometers to a little over 10 kilometers above the pulsar surface. We also find that the relationships between height and frequency of emission that follow from curvature radiation and from plasma-frequency emission could not be used to reproduce the observed frequency dependence of the width of the average intensity profiles.Comment: 15 pages, 9 figures, 8 tables, accepted for publication in A&

Standard Model with Cosmologically Broken Quantum Scale Invariance

We argue that scale invariance is not anomalous in quantum field theory, provided it is broken cosmologically. We consider a locally scale invariant extension of the Standard Model of particle physics and argue that it fits both the particle and cosmological observations. The model is scale invariant both classically and quantum mechanically. The scale invariance is broken cosmologically producing all the dimensionful parameters. The cosmological constant or dark energy is a prediction of the theory and can be calculated systematically order by order in perturbation theory. It is expected to be finite at all orders. The model does not suffer from the hierarchy problem due to absence of scalar particles, including the Higgs, from the physical spectrum.Comment: 13 pages, no figures significant revisions, no change in results or conclusion

Dynamics of threads and polymers in turbulence: power-law distributions and synchronization

We study the behavior of threads and polymers in a turbulent flow. These objects have finite spatial extension, so the flow along them differs slightly. The corresponding drag forces produce a finite average stretching and the thread is stretched most of the time. Nevertheless, the probability of shrinking fluctuations is significant and is known to decay only as a power-law. We show that the exponent of the power law is a universal number independent of the statistics of the flow. For polymers the coil-stretch transition exists: the flow must have a sufficiently large Lyapunov exponent to overcome the elastic resistance and stretch the polymer from the coiled state it takes otherwise. The probability of shrinking from the stretched state above the transition again obeys a power law but with a non-universal exponent. We show that well above the transition the exponent becomes universal and derive the corresponding expression. Furthermore, we demonstrate synchronization: the end-to-end distances of threads or polymers above the transition are synchronized by the flow and become identical. Thus, the transition from Newtonian to non-Newtonian behavior in dilute polymer solutions can be seen as an ordering transition.Comment: 13 pages, version accepted to Journal of Statistical Mechanic

The Angular Interval between the Direction of Progression and Body Orientation in Normal, Alcohol- and Cocaine Treated Fruit Flies

In this study we characterize the coordination between the direction a fruit-fly walks and the direction it faces, as well as offer a methodology for isolating and validating key variables with which we phenotype fly locomotor behavior. Our fundamental finding is that the angular interval between the direction a fly walks and the direction it faces is actively managed in intact animals and modulated in a patterned way with drugs. This interval is small in intact flies, larger with alcohol and much larger with cocaine. The dynamics of this interval generates six coordinative modes that flow smoothly into each other. Under alcohol and much more so under cocaine, straight path modes dwindle and modes involving rotation proliferate. To obtain these results we perform high content analysis of video-tracked open field locomotor behavior. Presently there is a gap between the quality of descriptions of insect behaviors that unfold in circumscribed situations, and descriptions that unfold in extended time and space. While the first describe the coordination between low-level kinematic variables, the second quantify cumulative measures and subjectively defined behavior patterns. Here we reduce this gap by phenotyping extended locomotor behavior in terms of the coordination between low-level kinematic variables, which we quantify, combining into a single field two disparate fields, that of high content phenotyping and that of locomotor coordination. This will allow the study of the genes/brain/locomotor coordination interface in genetically engineered and pharmacologically manipulated animal models of human diseases. © 2013 Gakamsky et al