Related papers: Comments on "Plasma oscillations and nonextensive …
The porous media equation has been proposed as a phenomenological ``non-extensive'' generalization of classical diffusion. Here, we show that a very similar equation can be derived, in a systematic manner, for a classical fluid by assuming…
The energy distribution and the energy fluctuation in the Tsallis canonical ensemble are studied with the OLM formalism but following a new way. The resulting formula for the energy fluctuation is not the same as that in previous work [Liu…
We carry out a systematic study of the dispersion relation for linear electrostatic waves in an arbitrarily degenerate quantum electron plasma. We solve for the complex frequency spectrum for arbitrary values of wavenumber $k$ and level of…
We investigate in this chapter the mathematical models for electromagnetic wave propagation in dispersive isotropic passive linear media for which the dielectric permittivity $\varepsilon$ and magnetic permeability $\mu$ depend on the…
We discuss a Tsallis distribution with complex nonextensivity parameter $q$. In this case the usual distribution is decorated with a log-periodic oscillating factor (apparently, such oscillations can bee seen in recently measured transverse…
Recently we have demostrated that the nonextensitivity parameter q occuring in some applications of Tsallis statistics (known also as index of the corresponding L\'evy distribution) is, in the q>1 case, given entirely by the fluctuations of…
In their recent Letter [Phys. Rev. Lett. 83, 4233 (1999)], Salazar and Toral (ST) study numerically a finite Ising chain with non-integrable interactions decaying like 1/r^(d+sigma) where -d <= sigma <= 0 (like ST, we discuss general…
This work presents a detailed study of the dispersion of capillary waves with small amplitude in viscous fluids using an analytically derived solution to the initial value problem of a small-amplitude capillary wave as well as direct…
The linear and nonlinear theories of electron-acoustic waves (EAWs) are studied in a partially degenerate quantum plasma with two-temperature electrons and stationary ions. The initial equilibrium of electrons is assumed to be given by the…
A linearized Vlasov-Poisson system of equations is transformed into a Schr\"{o}dinger equation, which is used to demonstrate that the fluctuation theorem holds for the relative stochastic entropy, defined in terms of the probability density…
A proof of the relativistic $H$-theorem by including nonextensive effects is given. As it happens in the nonrelativistic limit, the molecular chaos hypothesis advanced by Boltzmann does not remain valid, and the second law of thermodynamics…
The current form of Tsallis distribution for a Hamiltonian system with an arbitrary potential is found to represent a simple isothermal situation. In this letter, the q-exponential of a sum can be applied as the product of the q-exponential…
The evolution of an initial perturbation in Vlasov plasma is studied in the intrinsically nonlinear long-time limit dominated by the effects of particle trapping. After the possible transient linear exponential Landau damping, the evolution…
In these short, rather informal, expository notes I review the current state of the field regarding the mathematics of Landau damping, based on lectures given at the CIRM Research School on Kinetic Theory, November 14--18, 2022. These notes…
We propose a new and effective method to find plasma oscillatory and wave modes. It implies searching a pair of poles of two-dimensional (in coordinate $x$ and time $t$) Laplace transform of self-consistent plasma electric field $E(x,t) \to…
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,…
The limitation of the Quasilinear Theory (QLT) to describe the diffusion of electrons and ions in velocity space when interacting with a spectrum of large amplitude electrostatic Langmuir, Upper and Lower hybrid waves, is analyzed. We…
We examine the phenomenon of Landau Damping in relativistic plasmas via a study of the relativistic Vlasov-Poisson system (both on the torus and on $\mathbb{R}^3$) linearized around a sufficiently nice, spatially uniform kinetic…
I comment on a recent paper by Ruiz and Tsallis [Phys. Lett. A 376, 2451 (2012)] claiming to have found a '$q$-exponential' generalization of the large deviation principle for strongly correlated random variables. I show that the basic…
We have considered an expansion of solutions of the non-linear equations for both longitudinal and transverse waves in collisionless Maxwellian plasma in series of non-damping overtones of the field E(x,t) and electron velocity distribution…