Professor - Institute of Physics, University of São Paulo
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Current Projets
Quark-Gluon Plasma
- A new form of matter is produced at extremely high temperature and density, such as those obtained in high energy collisions of heavy-ions and possibly in proton-proton. The Large Hadron Collider, in CERN, is one of the places where this QGP matter is produced and lots of data are produced and can be analyzed, so we can learn more about the system formed at those collisions.In my work, We consider that this matter presents some fractal characteristics that allow us to understand many aspects of the data collected: the long-tail distributions of momentum and energy, which is described by the non-additive statistics. We try to answer the main question in this regard: what are the mechanisms that make the system behave according to the non-additive statistics, or Tsallis Statistics, instead of the standard Boltzmann-Gibbs Statistics. The fractal structure may be the answer to this question.
To understand how it happens, we introdiced the concept of Thermofractals.
Thermofractals
There are two types of thermofractals, each one with the following properties:
- 1) It is a thermodynamical system with total energy U=E+K, and a complex structure with a number N of compound systems that present the same properties as the parent system. Here, ε is the total internal energy of the N components, and K their total kinetic energy.
- 2) In the case of the thermofractal type-I, the internal energy, E, and the kinetic energy, K, of each compound system are such that the ratio ε/λ=E/K follows a distribution P(ε). In the case of the thermofractal type-II, the ratio ε/λ=E/U follows a distribution P(ε). Here, λ is a scaling parameter.
- 3) At some level of the internal structure, the fluctuations of the internal energy of the compound systems are small enough to be disregarded, and then their internal energy can be regarded as constant. The choice of the level is associated with λ and breaks the scaling symmetry.
The thermofractals present q-exponential distributions, and are best described by the non-additive entropy and the Tsallis Statistics. The entropic index, ''q'', in the Tsallis distribution can be calculated in terms of the parameters of the thermofractal structure, representing the number of degrees of freedom of the thermofractal.
In the context of particle physics, thermofractals were associated with the Non-extensive Self-consistent Thermodynamics theory, a generalization of the Self-Consistent Principle proposed by Rolf Hagedorn, resulting in the Non-extensive_self-consistent_thermodynamical_theory. The systems described by the Yang-Mills Theory allows the formation of thermofractal structures. A review on the subject can be found in the paper A. Deppman, E. Megias and D. P. Menezes, Structures of Yang-Mills Fields and Non-Extensive Statistics: Applications to High Energy Physics , Physics 2020, 2(3), 455-480.
Non-Extensive Self-Consistent Thermodynamics
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The Self-Consistent Thermodynamics, proposed by Rolf Ragedorn, is generalized to the non-extensive thermodynamics. The result is that it is possible to obtain a self-consistent thermodynamics with the non-additive entropy, that the particle energy and momentum distributions follow a q-exponential function, and a generalized Hagedorn Temperature is expected. This tempearture is associated to the phase transition point where the quark-gluon plasma is produced. Besides, a new hadron mass spectrum is obtained, which reproduces very well the observed hadronic states.
The paper can be freely downloaded through the link Non-Extensive Self-Consistent Thermodynamics
CRISP
adeppman@gmail.com