arXiv subjects

Airton Deppman

Publications and source records attributed to Airton Deppman.

At least 37 records · Page 2Linked to original sources

arXiv2020

Fractal Structures of Yang-Mills Fields and Non Extensive Statistics: Applications to High Energy Physics

In this work, we provide an overview of the recent investigations on the non-extensive Tsallis statistics and its applications to high energy physics and astrophysics, including physics at the Large Hadron Collider (LHC), hadron physics, and neutron stars. We review some recent investigations on the power-law distributions arising in high energy physics experiments focusing on a thermodynamic description of the system formed, which~could explain the power-law behavior. The possible connections with a fractal structure of hadrons is also discussed. The main objective of the present work is to delineate the state-of-the-art of those studies and~show some open issues that deserve more careful investigation. We propose several possibilities to test the theory through analyses of experimental data.

hep-ph↗

arXiv2020

Fractal structure of Yang-Mills fields

The origin of non-extensive thermodynamics in physical systems has been under intense debate for the last decades. Recent results indicate a connection between non-extensive statistics and thermofractals. After reviewing this connection, we analyze how scaling properties of Yang-Mills theory allow the appearance of self-similar structures in gauge fields. The presence of such structures, which actually behave as fractals, allows for recurrent non-perturbative calculations of vertices. It is argued that when a statistical approach is used, the non-extensive statistics is obtained, and the Tsallis entropic index, $q$, is deduced in terms of the field theory parameters. The results are applied to QCD in the one-loop approximation, resulting in a good agreement with the value of $q$ obtained experimentally.

hep-th↗

arXiv2019

Fractals, non-extensive statistics and QCD

In this work we analyse how scaling properties of Yang-Mills field theory manifest as self-similarity of truncated n-point functions by scale evolution. The presence of such structures, which actually behaves as fractals, allow for recurrent non-perturbative calculation of any vertex. Some general properties are indeed independent of the perturbative order, what simplifies the non-perturbative calculations. We show that for sufficiently high perturbative orders a statistical approach can be used, the non extensive statistics is obtained, and the Tsallis index, $q$, is deduced in terms of the field theory parameters. The results are applied to QCD in the one-loop approximation, where $q$ can be calculated, resulting in a good agreement with the value obtained experimentally. We discuss how this approach allows to understand some intriguing experimental findings in high energy collisions, as the behavior of multiplicity against collision energy, long-tail distributions and the fractal dimension observed in intermittency analysis.

hep-th↗

arXiv2019

Bag-type Model with Fractal Structure

In this work we present a bag-type model within a non-extensive statistics applied to the description of the properties of a hadronic system with an underlying fractal structure. The non-extensive ideal gas inside the bag is determined by the grand canonical partition function from which pressure, energy and particle density as well as temperature and chemical potential are obtained for the hadronic system. These quantities are studied in the approximation of fixed mass for all bag constituents but also for discrete and continuum masses. In all cases, the freeze-out line, corresponding to the energy per particle equal to 1 GeV and the lines corresponding to a fractal structure inside the proton volume are obtained. Finally, the pressure on the bag surface of the proton is calculated and the resulting value $(0.135\, {\rm GeV})^4$ obtained.

nucl-th↗

arXiv2019

Scaling properties of firearm homicides in Brazilian cities

The recent quantitative approaches for studing several aspects of urban life and infrastructure have shown that scale properties allow to understand many features of urban infrastructure and of human activity in cities. In this work, an analysis based on the complexity of cities network is performed for data on Brazilian cities firearms homicides. Due to the diversity in Brazilian population and cities, this is an interesting test for theories recently proposed. The superlinear power-law behavior for number of homicides as a function of city population, with exponent $β=1.15$ is obtained. The hypothesis that fractal structures can be formed in cities as well as in larger networks is tested, indicating that indeed self-similarity may be found in networks connecting several cities.

physics.soc-ph↗

arXiv2019

Fractal structure in Yang-Mills fields and non extensivity

Scaling properties of Yang-Mills fields are used to show that fractal structures are expected to be present in system described by those theories. We show that the fractal structure leads to recurrence formulas that allow the determination of non perturbative effective coupling. Fractal structures also cause the emergence of non extensivity in the system, which can be described by Tsallis statistics. The entropic index present in this statistics is obtained in terms of the field theory parameters. We apply the theory for QCD, and obtain the entropic index value, which is in good agreement with values obtained from experimental data. The Haussdorf dimension is calculated in terms of the entropic index, and the result for hadronic systems is in good agreement with the fractal dimension accessed by intermittency analysis of high energy collision data. The fractal dimension allow us to calculate the behavior of the particle multiplicity with the collision energy, showing again good agreement with data.

hep-th↗

arXiv2018

Fractal structure of hadrons and non-extensive statistics

The role played by non-extensive thermodynamics in physical systems has been under intense debate for the last decades. Some possible mechanisms that could give rise to non-extensive statistics have been formulated along the last few years, in particular the existence of a fractal structure in thermodynamic functions for hadronic systems. We investigate the properties of such fractal thermodynamical systems, in particular the fractal scale invariance is discussed in terms of the Callan-Symanzik~equation. Finally, we propose a diagrammatic method for calculations of relevant quantities.

hep-ph↗

arXiv2018

Fractal structure and non extensive statistics

The role played by non extensive thermodynamics in physical systems has been under intense debate for the last decades. With many applications in several areas, the Tsallis statistics has been discussed in details in many works and triggered an interesting discussion on the most deep meaning of entropy and its role in complex systems. Some possible mechanisms that could give rise to non extensive statistics have been formulated along the last several years, in particular a fractal structure in thermodynamics functions was recently proposed as a possible origin for non extensive statistics in physical systems. In the present work we investigate the properties of such fractal thermodynamical system and propose a diagrammatic method for calculations of relevant quantities related to such system. It is shown that a system with the fractal structure described here presents temperature fluctuation following an Euler Gamma Function, in accordance with previous works that evidenced the connections between those fluctuations and Tsallis statistics. Finally, the fractal scale invariance is discussed in terms of the Callan-Symanzik Equation.

cond-mat.stat-mech↗

arXiv2018

Renormalization group equation for Tsallis statistics

The non extensive statistics proposed by C. Tsallis has found wide applicability, being present even in the description of experimental data from high energy collisions. A system with a fractal structure in its energy-momentum space, named thermofractal, was shown to be described thermodynamically by the non extensive statistics. Due to the many common features between thermofractals and Hagedorn's fireballs, this system offers the possibility to investigate the origins of non extensivity in hadronic physics and in QCD. In this regard, the investigation of the scaling properties of thermofractals through the renormalization group equation, known as Callan-Symanzik equation, can be an interesting approach.

hep-ph↗

arXiv2017

Quark matter revisited with non extensive MIT bag model

In this work we revisit the MIT bag model to describe quark matter within both the usual Fermi-Dirac and the Tsallis statistics. We verify the effects of the non-additivity of the latter by analysing two different pictures: the first order phase transition of the QCD phase diagram and stellar matter properties. While, the QCD phase diagram is visually affected by the Tsallis statistics, the resulting effects on quark star macroscopic properties are barely noticed.

nucl-th↗

arXiv2016

Fractal aspects of hadrons

The non extensive aspects of $p_T$ distributions obtained in high energy collisions are discussed in relation to possible fractal structure in hadrons, in the sense of the thermofractal structure recently introduced. The evidences of self-similarity in both theoretical and experimental works in High Energy and in Hadron Physics are discussed, to show that the idea of fractal structure of hadrons and fireballs have being under discussion for decades. The non extensive self-consistent thermodynamics and the thermofractal structure allow one to connect non extensivity to intermittence and possibly to parton distribution functions in a single theoretical framework.

hep-ph↗

arXiv2016

Thermodynamics with fractal structure, Tsallis statistics and hadrons

A system presenting fractal structure in its thermodynamical functions is introduced, and it is shown that Tsallis statistics is the correct framework for describing the thermodynamical aspects of such fractal. Its Haussdorf dimension and its Lipshitz-Hölder exponent are determined in terms of the entropic index $q$. The connections with the intermittency in experimental data is discussed. The thermodynamical aspects of the thermofractal is related to the microscopic interaction of its components through the S-matrix.

hep-ph↗

arXiv2015

Non extensive thermodynamics and neutron star properties

In the present work we apply non extensive statistics to obtain equations of state suitable to describe stellar matter and verify its effects on microscopic and macroscopic quantities. Two snapshots of the star evolution are considered and the direct Urca process is investigated with two different parameter sets. $q$-values are chosen as 1.05 and 1.14. The equations of state are only slightly modified, but the effects are enough to produce stars with slightly higher maximum masses. The onsets of the constituents are more strongly affected and the internal stellar temperature decreases with the increase of the $q$-value, with consequences on the strangeness and cooling rates of the stars.

nucl-th↗

arXiv2014

Nonextensive thermodynamics for hadrons with finite chemical potentials

The non extensive thermodynamics of an ideal gas composed by bosons and/or fermions is derived from its partition function for systems with finite chemical potentials. It is shown that the thermodynamical quantities derived in the present work are in agreement with those obtained in previous works when $μ\le m$. However some inconsistencies of previous references are corrected when $μ> m$. A discontinuity in the first derivatives of the partition function and its effects are discussed in detail. We show that at similar conditions, the non extensive statistics provide a harder equation of state than that provided by the Boltzmann-Gibbs statistics.

hep-ph↗

arXiv2014

Nonextensive thermodynamics with finite chemical potentials and protoneutron stars

We derive the nonextensive thermodynamics of an ideal quantum gas composed by bosons and/or fermions with finite chemical potentials. We find agreement with previous works when $μ\le m$, and some inconsistencies are corrected for fermions when $μ> m$. This formalism is then used to study the thermodynamical properties of hadronic systems based on a Hadron Resonance Gas approach. We apply this result to study the protoneutron star stability under several conditions.

hep-ph↗

arXiv2013

Properties of hadronic systems according to the non-extensive self-consistent thermodynamics

The non-extensive self-consistent theory describing the thermodynamics of hadronic systems at high temperatures is used to derive some thermodynamical quantities, as pressure, entropy, speed of sound and trace-anomaly. The calculations are free of fitting parameters, and the results are compared to lattice QCD calculations, showing a good agreement between theory and data up to temperatures around 175 MeV. Above this temperature the effects of a singularity in the partition function at To = 192 MeV results in a divergent behaviour in respect with the lattice calculation.

hep-ph↗

arXiv2012

Systematic analysis of pT -distributions in p + p collisions

A systematic analysis of transverse momentum distribution of hadrons produced in ultra-relativistic p + p collisions is presented. We investigate the effective temperature and the entropic parameter from the non-extensive thermodynamic theory of strong interaction. We conclude that the existence of a limiting effective temperature and of a limiting entropic parameter is in accordance with experimental data.

hep-ex↗

arXiv2012

Self-consistency in non-extensive thermodynamics of highly excited hadronic states

The self-consistency of a thermodynamical theory for hadronic sys- tems based on the non-extensive statistics is investigated. We show that it is possible to obtain a self-consistent theory according to the asymptotic bootstrap principle if the mass spectrum and the energy density increase q-exponentially. A direct consequence is the existence of a limiting effective temperature for the hadronic system. We show that this result is in agreement with experiments.

math-ph↗