Instanton fermionic zero mode at finite temperature and chemical potential

In QCD the spontaneous breaking of chiral symmetry and the U(1) axial anomaly can be understood considering instantons as the gauge configurations mediating quark-quark interaction. The existence of an exact zero mode solution of the Dirac equation in the field of a single instanton is the fundamental ingredient of this analysis. Explicit expressions for psi_0 are available for T different from 0 and mu=0, and mu different from 0 and T=0. In this paper we derive the solution for the most general case T different from 0 and mu different from 0. This new result opens the possibility of investigating the QCD dynamics associated with instantons in the full phase diagram. As a first step in this direction we will study the dependence of the instanton density from the thermodynamic coordinates.Comment: 12 pages, 4 figures, Final version, accepted for publication on Phys. Rev.

Exploring the transition into the Chiral Regime of QCD using the Interacting Instanton Liquid Model

The non-perturbative quark-gluon interaction depends significantly on the value of the quark mass. In particular, in the light quark mass regime, correlations are strongly influenced by dynamics associated to chiral symmetry breaking. We use the Interacting Instanton Liquid Model (IILM) as a tool to investigate the microscopic dynamical mechanisms which underly the dependence on the quark mass and drive the transition into the chiral regime of QCD. To ensure the validity of the model, we first verify that the dependence on the quark mass for several observables calculated in the IILM agrees well with the predictions of chiral perturbation theory and with lattice simulations. We then show that a quark mass m*~80 MeV emerging naturally from the model specifies the mass scale above which the dynamics associated with low-lying eigenmodes of the Direac operator becomes sub-leading and the contribution of the fermion determinant is suppressed.Comment: contribution to XXV International Symposium on Lattice Field Theory, July 2007, Regensbur

Metropolis Monte Carlo on the Lefschetz thimble: application to a one-plaquette model

We propose a new algorithm based on the Metropolis sampling method to perform Monte Carlo integration for path integrals in the recently proposed formulation of quantum field theories on the Lefschetz thimble. The algorithm is based on a mapping between the curved manifold defined by the Lefschetz thimble of the full action and the flat manifold associated with the corresponding quadratic action. We discuss an explicit method to calculate the residual phase due to the curvature of the Lefschetz thimble. Finally, we apply this new algorithm to a simple one-plaquette model where our results are in perfect agreement with the analytic integration. We also show that for this system the residual phase does not represent a sign problem

Influence of augmented humans in online interactions during voting events

The advent of the digital era provided a fertile ground for the development of virtual societies, complex systems influencing real-world dynamics. Understanding online human behavior and its relevance beyond the digital boundaries is still an open challenge. Here we show that online social interactions during a massive voting event can be used to build an accurate map of real-world political parties and electoral ranks. We provide evidence that information flow and collective attention are often driven by a special class of highly influential users, that we name "augmented humans", who exploit thousands of automated agents, also known as bots, for enhancing their online influence. We show that augmented humans generate deep information cascades, to the same extent of news media and other broadcasters, while they uniformly infiltrate across the full range of identified groups. Digital augmentation represents the cyber-physical counterpart of the human desire to acquire power within social systems.Comment: 11 page

Sparse Predictive Structure of Deconvolved Functional Brain Networks

The functional and structural representation of the brain as a complex network is marked by the fact that the comparison of noisy and intrinsically correlated high-dimensional structures between experimental conditions or groups shuns typical mass univariate methods. Furthermore most network estimation methods cannot distinguish between real and spurious correlation arising from the convolution due to nodes' interaction, which thus introduces additional noise in the data. We propose a machine learning pipeline aimed at identifying multivariate differences between brain networks associated to different experimental conditions. The pipeline (1) leverages the deconvolved individual contribution of each edge and (2) maps the task into a sparse classification problem in order to construct the associated "sparse deconvolved predictive network", i.e., a graph with the same nodes of those compared but whose edge weights are defined by their relevance for out of sample predictions in classification. We present an application of the proposed method by decoding the covert attention direction (left or right) based on the single-trial functional connectivity matrix extracted from high-frequency magnetoencephalography (MEG) data. Our results demonstrate how network deconvolution matched with sparse classification methods outperforms typical approaches for MEG decoding

Thermodynamics of a three-flavor nonlocal Polyakov--Nambu--Jona-Lasinio model

The present work generalizes a nonlocal version of the Polyakov loop-extended Nambu and Jona-Lasinio (PNJL) model to the case of three active quark flavors, with inclusion of the axial U(1) anomaly. Gluon dynamics is incorporated through a gluonic background field, expressed in terms of the Polyakov loop. The thermodynamics of the nonlocal PNJL model accounts for both chiral and deconfinement transitions. Our results obtained in mean-field approximation are compared to lattice QCD results for $N_\text{f}=2+1$ quark flavors. Additional pionic and kaonic contributions to the pressure are calculated in random phase approximation. Finally, this nonlocal 3-flavor PNJL model is applied to the finite density region of the QCD phase diagram. It is confirmed that the existence and location of a critical point in this phase diagram depends sensitively on the strength of the axial U(1) breaking interaction.Comment: 31 pages, 15 figures, minor changes compared to v

Thermodynamics and quark susceptibilities: a Monte-Carlo approach to the PNJL model

The Monte-Carlo method is applied to the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. This leads beyond the saddle-point approximation in a mean-field calculation and introduces fluctuations around the mean fields. We study the impact of fluctuations on the thermodynamics of the model, both in the case of pure gauge theory and including two quark flavors. In the two-flavor case, we calculate the second-order Taylor expansion coefficients of the thermodynamic grand canonical partition function with respect to the quark chemical potential and present a comparison with extrapolations from lattice QCD. We show that the introduction of fluctuations produces only small changes in the behavior of the order parameters for chiral symmetry restoration and the deconfinement transition. On the other hand, we find that fluctuations are necessary in order to reproduce lattice data for the flavor non-diagonal quark susceptibilities. Of particular importance are pion fields, the contribution of which is strictly zero in the saddle point approximation