Kamel Ourabah

• PhD
• University of Sciences and Technology Houari Boumediene

Non-Maxwellian distributions are commonly observed across a wide range of systems and scales. While direct observations provide the strongest evidence for these distributions, they also manifest indirectly through their influence on processes and quantities that strongly depend on the energy distribution, such as reaction rates. In this paper, we i...

Non-Maxwellian distributions are commonly observed across a wide range of systems and scales. While direct observations provide the strongest evidence for these distributions, they also manifest indirectly through their influence on processes and quantities that strongly depend on the energy distribution, such as reaction rates. In this paper, we i...

It has recently been demonstrated (Giusti in Phys Rev D 101:124029, 2020, https://doi.org/10.1103/PhysRevD.101.124029 ) that characteristic traits of Milgrom’s modified Newtonian dynamics (MOND) can be replicated from an entirely distinct framework: a fractional variant of Newtonian mechanics. To further assess its validity, this proposal needs to...

La mécanique quantique offre des prédictions remarquablement précises sur le monde microscopique, mais son interprétation suscite de nombreux débats, tant parmi les physiciens que parmi les philosophes.Certitudes et incertitudes en mécanique quantique met en lumière ce contraste entre la certitude des prédictions de la théorie quantique et l’incert...

It has recently been demonstrated [A. Giusti, Phys. Rev. D 101, 124029 (2020)] that characteristic traits of Milgrom's modified Newtonian dynamics (MOND) can be replicated from an entirely distinct framework: a fractional variant of Newtonian mechanics. To further assess its validity, this proposal needs to be tested in relevant astrophysical scena...

In many plasma environments, e.g., in the solar wind, collisions between particles are rare, challenging therefore the assumption of strict equilibrium. In this paper, we propose to model such nonequilibrium plasmas as a collection of small subsystems that remain infinitely close to equilibrium. This allows us to describe their statistical properti...

The Lindley distribution is useful in a wide variety of fields, such as biology and astronomy. Many generalizations of the Lindley distribution have been introduced in the literature, with various motivations. Inspired by the concept of superstatistics in nonequilibrium statistical mechanics, we introduce here a novel generalization of the Lindley...

Distributions that deviate from equilibrium predictions are commonly observed across a broad spectrum of systems, ranging from laboratory experiments to astronomical phenomena. These distributions are generally regarded as a manifestation of a quasiequilibrium state and can very often be represented as a superposition of statistics, i.e., superstat...

Since the seminal work of Verlinde, the idea that gravity may be an emergent force of entropic origin has gained widespread attention. Many generalizations of this key idea have been considered in the literature, starting from well-known and well-motivated generalized entropies to derive generalized gravity theories. Here, we approach the problem f...

We study the Jeans gravitational instability for a mixture of baryonic and dark matter particles, in the post-Newtonian approximation. We adopt a kinetic model consisting of a coupled system of post-Newtonian collisionless Boltzmann equations, for each species, coupled to the post-Newtonian Poisson equations. We derive the stability criterion, acco...

The Universe is made up of systems consisting of a very large number of particles interacting in a very complex way. When studying these systems, a precise microscopic approach is unattainable. In practice, the best strategy is one that is able to “distinguish” between superfluous information and the information needed to make predictions about the...

Since the seminal work of Verlinde, the idea that gravity may be an emergent force of entropic origin has gained widespread attention. Many generalizations of this key idea have been considered in the literature, starting from well-known and well-motivated generalized entropies to derive generalized gravity theories. Here, we approach the problem f...

Quasiequilibrium systems, exhibiting only local equilibrium, can be represented as a collection of sub-systems that remain infinitely close to equilibrium. Such a methodological attitude is particularly well-motivated for gravity-dominated systems. Here we explore the consequences of quasiequilibrium states on two theoretical conditions of interest...

We study the Jeans gravitational instability for a mixture of baryonic and dark matter particles, in the post-Newtonian approximation. We adopt a kinetic model consisting of a coupled system of post-Newtonian collisionless Boltzmann equations, for each species, coupled to the post-Newtonian Poisson equations. We derive the stability criterion, acco...

We discuss the hydrodynamic representation of a wide class of quantum media exhibiting similar elementary excitations and dispersion properties. The representation covers quantum systems characterized by any type of (long-range) self-interaction, associated with an arbitrary potential. It also accounts for possible nonlinearities, which may arise,...

We present a quantum treatment of the Jeans gravitational instability in the Newtonian limit of the non-minimal matter-curvature coupling gravity model. By relying on Wigner functions, allowing for the representation of quantum states in a classical phase space, we formulate a quantum kinetic treatment of this problem, generalizing the classical ki...

L’Univers est fait de systèmes composés d’un très grand nombre de particules interagissant de manière complexe. Lors de l’étude de tels systèmes, une approche microscopique exacte est hors de portée. En pratique, la meilleure stratégie est celle qui saura « faire le tri » entre l’information superflue et l’information nécessaire pour prédire leur é...

A singularity-free generalisation of Newtonian gravity can be constructed (Lazar in Phys Rev D 102:096002, 2020) within the framework of gradient field theory. This procedure offers a straightforward regularisation of Newtonian gravity and remains equally well applicable to other fields, such as electromagnetic fields. Here, with the aim of finding...

We discuss the hydrodynamic representation of a wide class of quantum media exhibiting similar elementary excitations and dispersion properties. The representation covers quantum systems characterized by any type of (long-range) self-interaction, associated with an arbitrary potential. It also accounts for possible nonlinearities, which may arise e...

We study the Jeans-type gravitational instability for a self-gravitating medium composed of two species, baryonic (bright) and dark matter particles, using a hybrid quantum-classical fluid approach. Baryonic matter is treated classically, which is appropriate for most astrophysical environments , e.g., Bok globules, while dark matter is treated thr...

The observed distributions of stellar parameters, in particular, rotational and radial velocities, often depart from the Maxwellian (Gaussian) distribution. In the absence of a consistent statistical framework, these distributions are, in general, accounted for phenomenologically by employing power-law distributions, such as Tsallis or Kaniadakis d...

We present a quantum treatment of the Jeans gravitational instability in the Newtonian limit of the non-minimal matter-curvature coupling gravity model. By relying on Wigner functions, allowing for the representation of quantum states in a classical phase space, we formulate a quantum kinetic treatment of this problem, generalizing the classical ki...

We study the Jeans-type gravitational instability for a self-gravitating medium composed of two species, baryonic (bright) and dark matter particles, using a hybrid quantum-classical fluid approach. Baryonic matter is treated classically, which is appropriate for most astrophysical environments, e.g., Bok globules, while dark matter is treated thro...

This paper addresses the process of Jeans gravitational instability in the framework of Eddington-inspired Born-Infeld (EiBI) theory, by accounting for quantum effects. In the Newtonian limit, the model reduces to a generalized Schrödinger-Poisson model, which is treated in two different ways: from a quantum hydrodynamic approach and from a quantum...

We correct a typographical error in Eq. (9) and retract the conclusion in Section 3.1; i.e., the argument-Schrödinger equation with imaginary classicality-enforcing potential Eq. (5) does not admit a Gaussian travelling wave solution.

Distributions different from those predicted by equilibrium statistical mechanics are commonplace in a number of physical situations, such as plasmas and self-gravitating systems. The best strategy for probing these distributions and unavailing their origins consists in combining theoretical knowledge with experiments, involving both direct and ind...

We focus on the traveling wave solutions for the Schrödinger equations with a logarithmic nonlinearity; i.e., the argument Schrödinger equation or the Kostin equation. We show that when the argument Schrödinger equation has an additional nonlinear term of the so-called classicality-enforcing potential it admits traveling wave solutions of the Gauss...

The generalized uncertainty principle (GUP) is a generalization of the Heisenberg principle motivated by several theories of quantum gravity such as string theory. It predicts the existence of a minimal distance and/or maximum momentum. Here, we study some consequences of the GUP in the context of the statistical mechanics of self-gravitating fermi...

In the Newtonian regime, the dynamics of scalar field dark matter is governed by the Schrödinger-Poisson model. In the usual treatment, the model is represented in a hydrodynamic form, by introducing macroscopic quantities such as the density and the average velocity. Here, we discuss an alternative kinetic representation of the same model, by rely...

In many quantum gravity theories, there is the emergence of a generalized uncertainty principle (GUP), implying a minimal length of the order of the Planck length. From the statistical mechanics point of view, this prescription enters into the phase space structure by modifying the elementary cell volume, which becomes momentum-dependent. In this l...

Because of the long-range nature of the gravitational interaction, self-gravitating systems never reach thermal equilibrium in the thermodynamic limit but remain trapped in nonequilibrium stationary states, or quasiequilibrium states. Here, we deal with quasiequilibrium self-gravitating systems by representing them as a collection of smaller subsys...

Inspired by the theory of scale relativity, a nonlinear Schrödinger equation has been recently proposed to model dark matter halos. The equation involves a logarithmic nonlinearity associated with an effective temperature and a source of dissipation. Herein, we study the Benjamin–Feir type modulational instability exhibited by this model. We extend...

Motivated by the recent result by Davis et al. [Phys. Rev. E 100, 023205 (2019)] that velocity distributions of collisionless steady-state plasmas must follow superstatistics, we examine systematically the ability of superstatistics to account for observations of anomalous distributions in plasma physics. We consider the two possible scenarios: the...

According to the theory of scale relativity, dark matter halos can be described through a generalized Schrödinger equation, involving a logarithmic non-linearity associated with an effective temperature and a source of dissipation. This wave equation can be written, via the Madelung transformation, in the form of a quantum hydrodynamic model which,...

We explore the effect of temperature fluctuations on continuous-variable quantum systems, with particular interest in wave packet dynamics, entanglement properties, and the standard quantum limit. Our method relies on the formalism of superstatistics and consists in the superposition of a distribution \(f(\beta )\), characterizing fluctuations, ove...

Many quantum gravity theories predict a minimal length of the order of the Planck length. This prescription implies a numberof modifications in the phase space structure that have consequences on any statistical mechanics approach. We have recently introduced (Shababi and Ourabah, 2019) a formulation of the Thomas–Fermi model in consistency with th...

Fluctuations can be incorporated into an equilibrium statistical mechanics setting through a superposition of different statistics, i.e., superstatistics. Herein, we have combined equipartition theorems arising out of superstatistics together with the holographic principle, to address the main consequences of fluctuations on gravitation and cosmolo...

Many quantum gravity theories predict a minimal length of the order of the Planck length. In this letter, the Thomas–Fermi model is reformulated by taking into account such a prescription. A generalized Thomas–Fermi equation is derived, that reduces to the usual one in the absence of a minimal length. As an application, the model is used to study t...

In this paper, I study the effect of a small deviation from the Fermi–Dirac statistics on the quantum ion acoustic waves. For this purpose, a quantum hydrodynamic model is developed based on the Polychronakos statistics, which allows for a smooth interpolation between the Fermi and Bose limits, passing through the case of classical particles. The m...

Through a kinetic approach, in which temperature fluctuations are taken into account, we obtain generalized fractional statistics interpolating between Fermi-Dirac and Bose-Einstein statistics. The latter correspond to the superstatistical analogues of the Polychronakos and Haldane-Wu statistics. The virial coefficients corresponding to these stati...

Many complex systems exhibiting fluctuations can be described by decomposing their dynamics at different scales. Their statistical properties are then given by a mixture of statistics, i.e., superstatistics. In this paper, we study quantum entanglement in a system, obeying a superstatitical model. Such an approach is expected to be a suitable appro...

Nous présentons ici une autre façon de traiter les systèmes hors équilibre . C'est une méthode macroscopique où il faut subdiviser le système en cellules de sorte que chacune d'entre elles représente un système à l'équilibre . La température fluctue et obéit à une loi de probabilité . En faisant un choix judicieux de cette loi on retrouve des fonct...

In this paper, we consider entanglement in a system out of equilibrium, adopting the viewpoint given by the formalism of superstatistics. Such an approach yields a good effective description for a system in a slowly fuctuating environment, within a weak interaction between the system and the environment. For this purpose, we introduce a new version...

We rely on our proof of the non-decreasing character of quantum Kaniadakis entropy under projective measurement [Phys. Rev. E 92, 032114 (2015)], and put it into perspective with the results of Bosyk et al. [arXiv:1506.02090]. Our method, adopted for the proof that Kaniadakis entropy does not decrease under a projective measurement, is based on the...

Ce polycopié se veut être une introduction à la physique statistique non- extensive. En guise d'applications, nous avons délibérément choisi de ne présenter que certains de nos résultats de recherche ayant trait à la distribution de Fermi-Dirac non-extensive. Celle-ci est une généralisation à un paramètre de la distribution bien connue de Fermi-Dir...

La statistique non extensive de Tsallis, généralisation à un seul paramètre de la statistique de Boltzmann- Gibbs, a récemment connu un grand regain d’intérêt. On se propose dans ce travail de présenter un état de l’art de cette nouvelle statistique en insistant sur son contexte, ses fondements, ses domaines d’application et surtout sur la nécessit...

It is well-known that the von Neumann entropy of a quantum state does not decrease with a projective measurement. This property holds for Tsallis and Rényi entropies as well. In this brief report, we show that the recently introduced quantum version of the Kaniadakis entropy preserves this property.

A first use of the Kaniadakis entropy in the context of quantum information is presented. We first show that (as all smooth and concave trace-form entropies) it exhibits some properties allowing it to be a possible candidate for a generalized quantum information theory. We then use it to determine the degree of entanglement. The influence of the pa...

We propose to put the well-known nonthermal and suprathermal empirical distributions, used in plasma physics, onto a more rigorous foundation. Their use is frequently criticized because of a lack of formal derivation and physical explanation. A connection between these non-Maxwellian distributions and the Beck-Cohen superstatistics is suggested. Th...

We propose to put the well-known nonthermal and suprathermal empirical distributions, used in plasma physics, onto a more rigorous foundation. Their use is frequently criticized because of a lack of formal derivation and physical explanation. A connection between these non-Maxwellian distributions and the Beck-Cohen superstatistics is suggested. Th...

Blackbody radiation is reconsidered using the counterpart of the Bose-Einstein distribution in the κ statistics arising from the Kaniadakis entropy. The generalized Planck radiation law is presented and compared to the usual law, to which it reduces in the limiting case κ→0. Effective Einstein's coefficients of emission and absorption are defined i...

Using the generalized Fermi–Dirac distribution function arising from Tsallis statistical mechanics, we revisit the Sommerfeld model for metallic elements. The chemical potential, the total energy and the heat capacity are calculated. It is shown that the linearity between the heat capacity and the temperature is q-dependent, where q stands for the...

Weak dust ion-acoustic (DIA) double- layers (DLs) in a dusty plasma with nonextensive electrons are addressed. A generalized Korteweg-de Vries equation with a cubic nonlinearity is derived. It is shown that under certain conditions, the effect of electron nonextensivity can be quite important. In particular, it may be noted that due to the net nega...

Quantum ion-acoustic solitary waves are studied by considering the effects of exchange and correlation for the electrons. Starting from one-dimensional quantum hydrodynamic equations, including the term of exchange correlation for electrons, we obtain a model in which two dimensionless parameters appear (in addition to the parameter measuring the q...

The nonextensive Thomas–Fermi model with thermal effects is extended to the case of atoms within a large magnetic field. A generalization of the Thomas–Fermi equation is derived. The virial theorem is verified and the dielectric screening process is revisited in the present extended model. Some comparisons are made with the case without a magnetic...

The Thomas–Fermi approach for self-gravitating fermions is revisited within the theoretical framework of the qq-statistics. Starting from the qq-deformation of the Fermi–Dirac distribution function, a generalized Thomas–Fermi equation is derived. It is shown that the Tsallis entropy preserves a scaling property of this equation. The qq-statistical...

The dielectric screening process is revisited within the theoretical framework of the nonextensive Thomas-Fermi model with thermal effects. The nonextensive counterpart of the Fermion distribution function is used. It is found that the nonextensive corrections (which vanish in the zero-temperature limit) are more noticeable as the nonextensive char...