arXiv subjects

Fernando Haas

Publications and source records attributed to Fernando Haas.

At least 19 recordsLinked to original sources

arXiv2024

On the Damped Pinney Equation from Noether Symmetry Principles

There are several versions of the damped form of the celebrated Pinney equation, which is the natural partner of the undamped time-dependent harmonic oscillator. In this work these dissipative versions of the Pinney equation are briefly reviewed. We show that Noether's theorem for the usual time-dependent harmonic oscillator as a guiding principle for derivation of the Pinney equation also works in the damped case, selecting a Noether symmetry based damped Pinney equation. The results are extended to general nonlinear damped Ermakov systems. A certain time-rescaling always allows to remove the damping from the final equations.

physics.class-ph↗

arXiv2024

Two-dimensional Fireballs as a Lagrangian Ermakov System

The equations of motion for the variance of strictly one-dimensional or two-dimensional non-relativistic fireballs are derived, from the hydrodynamic equations for an ideal, structureless Boltzmann gas. For this purpose a Gaussian number density {\it Ansatz} is applied, together with low-dimensional proposals for the energy density, coherent with the equipartition theorem. The resulting ordinary differential equations are shown to admit a variational formulation. The underlying symmetries are connected to constants of motion, through Noether's theorem. The two-dimensional case is special, corresponding to a Lagrangian Ermakov system without external forcing. There is a comparison with the fully three-dimensional fireballs, and its reduction to effective two-dimensional dynamical system for elliptic trajectories. The exact analytical solutions are worked out.

math-ph↗

arXiv2024

Methodological notes on the gauge invariance in the treatment of waves and oscillations in plasmas $via$ the Einstein-Vlasov-Maxwell system: Fundamental equations

The theory of gauge transformations in linearized gravitation is investigated. After a brief discussion of the fundamentals of the kinetic theory in curved spacetime, the Einstein-Vlasov-Maxwell system of equations in terms of gauge invariant quantities is established without neglecting the equations of motion associated with the dynamics of the non-radiative components of the metric tensor. The established theory is applied to a non-collisional electron-positron plasma, leading to a dispersion relation for gravitational waves in this model system. The problem of Landau damping is addressed and some attention is given to the issue of the energy exchanges between the plasma and the gravitational wave. In a future paper, a more complete set of approximate dispersion relations for waves and oscillations in plasmas will be presented, including the dynamics of non-radiative components of the metric tensor, with special attention to the problems of the Landau damping and of the energy exchanges between matter, the electromagnetic field and the gravitational field.

physics.plasm-ph↗

arXiv2024

Derivation of Dirac Exchange Interaction Potential from Quantum Plasma Kinetic Theory

The Dirac exchange interaction is derived from recent quantum kinetic theory for collisionless plasmas. For this purpose, the kinetic equation is written in the semiclassical and long wavelength approximations. The validity of the model for real systems is worked out, in terms of temperature and density parameters. Within the region of applicability, the correlation potential energy is shown to be always smaller than the exchange contribution. From the moments of the quantum kinetic equations, macroscopic, hydrodynamic equations are found, for an electron-ion plasma. The Dirac exchange term is explicitly derived, in the case of a completely degenerate electron gas. These results show, within quantum kinetic theory for charged particle systems, a new view of the Dirac exchange interaction frequently used in density functional theory parametrization. Finally, a simpler form of the quantum plasma exchange kinetic theory is also found.

physics.plasm-ph↗

arXiv2023

Compton Scattering of Plasmons

We extend de concept of Compton scattering to the case of plasmons. This concept was originally applied to electrons in vacuum. Here, we consider electrons in a plasma, and study the scattering properties of photon-plasmon interactions. We show that a number $n$ of plasmons with frequency $ \omega \simeq \omega_p$ is scattered by an electron, for an incident photon with frequency $\omega' \geq \omega_p$, where $\omega_p$ is the plasma frequency. We describe the general case of arbitrary $n$ and assume that Compton scattering of plasmons is intrinsically a nonlinear process. Our theoretical model is based on Volkov solutions of the Klein-Gordon equation describing the state of relativistic electrons, when the spin is ignored. We derive the corresponding scattering probability, as well as the recoil formula associated with arbitrary the final electron states. This process can be relevant to intense laser plasma interactions.

physics.plasm-ph↗

arXiv2023

Electron Holes in a Regularized Kappa Background

The pseudopotential method is used to derive electron hole structures in a suprathermal plasma having a regularized $\kappa$ probability distribution function background. The regularized character allows the exploration of small $\kappa$ values beyond the standard suprathermal case, for which $\kappa > 3/2$ is a necessary condition. We have found the nonlinear dispersion relation yielding the amplitude of the electrostatic potential in terms of the remaining parameters, in particular the drift velocity, the wavenumber and the spectral index. Periodic, solitary wave, drifting and non-drifting solutions have been identified. In the linear limit, the dispersion relation yields generalized Langmuir and electron acoustic plasma modes. Standard electron hole structures are regained in the $\kappa \gg 1$ limit.

physics.plasm-ph↗

arXiv2023

Noether symmetries and conservation laws of a reduced gauged bilayer graphene model

A canonical Hamiltonian is found for a reduced version of the Jackiw-Pi model for bilayer graphene. From the corresponding Lagrangian, the Noether point symmetries and conserved quantities are determined. The Noether symmetry group is the same as the fifth-dimensional group for the time-dependent harmonic oscillator. The realization of the algebra is achieved in terms of just one particular solution $g_1$ of the time-dependent harmonic oscillator equation underlying the reduced Jackiw-Pi model. Some numerical solutions are worked out.

math-ph↗

arXiv2023

Probing modified plasma waves in non-linear electrodynamics

Properties of modified plasma waves in non-linear electrodynamics are investigated. We consider a cold, uniform, collisionless, and magnetized plasma model. Initially, we also assume small amplitude waves and the non-relativistic approximation. For electrostatic waves, we obtain a modified Trivelpiece-Gould dispersion relation with a suitable change in the plasma frequency and analyze the stability of modes. Furthermore, electromagnetic waves related to the generalized Appleton-Hartree equation are established. In this case, we discuss modifications in circularly polarized waves, ordinary and extraordinary modes. After that, we apply our results to particular cases of low-energy quantum electrodynamics and a generalized Born-Infeld model. The correspondent dispersion relations and effects on the propagation regions are determined. Finally, we include the relativistic and large amplitude effects for circularly polarized waves. We obtain the dispersion relation within effective non-linear electrodynamics and examine the behavior of the refractive index when the frequency of the propagating wave converges to the plasma frequency.

physics.plasm-ph↗

arXiv2022

Linear and nonlinear waves in quantum plasmas with arbitrary degeneracy of electrons

The purpose of this review is to revisit recent results in the literature where quantum plasmas with arbitrary degeneracy degree are considered. This is different from a frequent approach, where completely degeneracy is assumed in dense plasmas. The general reasoning in the reviewed works is to take a numerical coefficient in from of the Bohm potential term in quantum fluids, in order to fit the linear waves from quantum kinetic theory in the long wavelength limit. Moreover, the equation of state for the ideal Fermi gas is assumed, for arbitrary degeneracy degree. The quantum fluid equations allow the expedite derivation of weakly nonlinear equations from reductive perturbation theory. In this way, quantum Korteweg - de Vries and quantum Zakharov - Kuznetsov equations are derived, together with the conditions for bright and dark soliton propagation. Quantum ion-acoustic waves in unmagnetized and magnetized plasmas, together with magnetosonic waves, have been obtained for arbitrary degeneracy degree. The conditions for the application of the models, and the physical situations where the mixed dense - dilute systems exist, have been identified.

physics.plasm-ph↗

arXiv2021

Dynamics of antiproton plasma in a time-dependent harmonic trap

An antiproton plasma confined in a quasi-1D device is described in terms of a self-consistent fluid formulation using a variational approach. Unlike previous treatments, the use of the time-dependent variational method allows to retain the thermal and Coulomb effects. A certain Ansatz is proposed for the number density and fluid velocity fields, which reduces the problem essentially to ordinary nonlinear differential equations. In adiabatic cooling, the frequency of the trap potential is slowly decreased. An adiabatic equation of state is assumed for closure. The numerical simulation of the nonlinear dynamics is performed, for realistic parameters.

physics.plasm-ph↗

arXiv2021

Electron Holes in a $\kappa$ Distribution Background with Singularities

The pseudo-potential method is applied to derive diverse propagating electron hole structures, in a nonthermal or $\kappa$ particle distribution function background. The associated distribution function Ansatz reproduces the Schamel distribution of \cite{Schamel2015} in the Maxwellian ($\kappa \rightarrow \infty$) limit, providing a significant generalization of it for plasmas where superthermal electrons are ubiquitous, such as space plasmas. The pseudo-potential and the nonlinear dispersion relation are evaluated. The role of the spectral index $\kappa$ on the nonlinear dispersion relation is investigated, in what concerns the wave amplitude for instance. The energy-like first integral from Poisson's equation is applied to analyze the properties of diverse classes of solutions: with the absence of trapped electrons, with a non-analytic distribution of trapped electrons, or with a surplus of trapped electrons. Special attention is therefore paid to the non-orthodox case where the electrons distribution function exhibits strong singularities, being discontinuous or non-analytic.

physics.plasm-ph↗

arXiv2021

Exchange fluid model derived from first principles quantum kinetic theory for plasmas

Starting from first principles quantum kinetic theory for ideal plasmas with exchange effects, the quantum hydrodynamic equations are derived taking moments of the corresponding exchange-Vlasov equation. The case of an electron-ion plasma where ions are entirely classical is considered. The linear dispersion relation for ion-acoustic waves is found from the macroscopic equations and compared with exchange quantum kinetic theory, yielding a qualitative agreement apart from a numerical factor of order one in the exchange contribution, assuming a Maxwellian background as a first step, for analytical simplicity. The validity conditions of the treatment are discussed and exchange effects are shown to be necessarily a correction, within the ideal and long wavelength approximations.

physics.plasm-ph↗

arXiv2021

Bernstein-Greene-Kruskal approach for the quantum Vlasov equation

The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables, similarly as in the solution of the Vlasov-Poisson system by means of the Bernstein-Greene-Kruskal method. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed and shown to be immediately integrable up to a recursive chain of quadratures in position space only. { As it stands, the treatment of the self-consistent, Wigner-Poisson system is beyond the scope of the method, which assumes} a given smooth { time-independent} external potential. Accuracy tests for the series expansion are also provided. Examples of anharmonic potentials are worked out up to a high order on the quantum diffraction parameter.

quant-ph↗

arXiv2021

Relativistic Ermakov-Milne-Pinney Systems and First Integrals

The Ermakov-Milne-Pinney equation is ubiquitous in many areas of physics that have an explicit time-dependence, including quantum systems with time dependent Hamiltonian, cosmology, time-dependent harmonic oscillators, accelerator dynamics, etc. The Eliezer and Gray physical interpretation of the Ermakov-Lewis invariant is applied as a guiding principle for the derivation of the special relativistic analog of the Ermakov-Milne-Pinney equation and associated first integral. The special relativistic extension of the Ray-Reid system and invariant is obtained. General properties of the relativistic Ermakov-Milne-Pinney are analyzed. The conservative case of the relativistic Ermakov-Milne-Pinney equation is described in terms of a pseudo-potential, reducing the problem to an effective Newtonian form. The non-relativistic limit is considered as well. A relativistic nonlinear superposition law for relativistic Ermakov systems is identified. The generalized Ermakov-Milne-Pinney equation has additional nonlinearities, due to the relativistic effects.

math-ph↗

arXiv2018

Modified plasma waves described by a logarithmic electrodynamics

The propagation of plasma waves in a new non-linear, logarithmic electrodynamics model is performed. A cold, uniform, collisionless fluid plasma model is applied. Electrostatic waves in magnetized plasma are shown to correspond to modified Trivelpiece-Gould modes, together with changes of the plasma and upper-hybrid frequencies, driven by the logarithmic electrodynamics effects. Electromagnetic waves are described by a generalized Appleton-Hartree dispersion relation. The cases of propagation parallel or perpendicular to the equilibrium magnetic field are analyzed in detail. In particular, generalized ordinary and extraordinary modes are obtained. We determine the changes, due to logarithmic electrodynamics, in the allowable and forbidden frequency bands of the new extraordinary mode. Estimates are provided about the strength of the ambient magnetic field, so that the non-linear electrodynamics effects become decisive.

physics.plasm-ph↗

arXiv2017

Neutrino magnetohydrodynamics

A new neutrino magnetohydrodynamics (NMHD) model is formulated, where the effects of the charged weak current on the electron-ion magnetohydrodynamic fluid are taken into account. The model incorporates in a systematic way the role of the Fermi neutrino weak force in magnetized plasmas. A fast neutrino-driven short wavelengths instability associated with the magnetosonic wave is derived. Such an instability should play a central role in strongly magnetized plasma as occurs in supernovae, where dense neutrino beams also exist. In addition, in the case of nonlinear or high frequency waves, the neutrino coupling is shown to be responsible for breaking the frozen-in magnetic field lines condition even in infinite conductivity plasmas. Simplified and ideal NMHD assumptions were adopted and analyzed in detail.

physics.plasm-ph↗

arXiv2017

Effective photon mass and exact translating quantum relativistic structures

Using a variation of the celebrated Volkov solution, the Klein-Gordon equation for a charged particle is reduced to a set of ordinary differential equations, exactly solvable in specific cases. The new quantum relativistic structures can reveal a localization in the radial direction perpendicular to the wave packet propagation, thanks to a non-vanishing scalar potential. The external electromagnetic field, the particle current density and the charge density are determined. The stability analysis of the solutions is performed by means of numerical simulations. The results are useful for the description of a charged quantum test particle in the relativistic regime, provided spin effects are not decisive.

physics.plasm-ph↗

arXiv2017

A new two-stream instability mode in magnetized quantum plasma

A new transverse mode in a two-stream magnetized quantum plasma is studied by means of a quantum hydrodynamic model, under non-relativistic and ideal Fermi gas assumptions. It is found that Fermi pressure effects induce a minimum cutoff wavelength for instability, unlike the classical case which is unstable for larger wavenumbers. The external magnetic field is also shown to produce a stabilizing effect. Conditions for the applicability of the model and specific parameters for experimental observations are thoroughly discussed.

physics.plasm-ph↗