Fernando Haas

A magnetohydrodynamic model for quantum plasmas

The quantum hydrodynamic model for charged particle systems is extended to the cases of nonzero magnetic fields. In this way, quantum corrections to magnetohydrodynamics are obtained starting from the quantum hydrodynamical model with magnetic fields. The importance of the quantum corrections is described by a parameter H which can be significant in dense astrophysical plasmas. The quantum magnetohydrodynamic model is analyzed in the infinite conductivity limit. The conditions for equilibrium in ideal quantum magnetohydrodynamics are established. Translationally invariant exact equilibrium solutions are obtained in the case of the ideal quantum magnetohydrodynamic model.

Modified Zakharov equations for plasmas with a quantum correction

Quantum Zakharov equations are obtained to describe the nonlinear interaction between quantum Langmuir waves and quantum ion-acoustic waves. These quantum Zakharov equations are applied to two model cases, namely, the four-wave interaction and the decay instability. In the case of the four-wave instability, sufficiently large quantum effects tend to suppress the instability. For the decay instability, the quantum Zakharov equations lead to results similar to those of the classical decay instability except for quantum correction terms in the dispersion relations. Some considerations regarding the nonlinear aspects of the quantum Zakharov equations are also offered.

Nonlinear structures: Explosive, soliton, and shock in a quantum electron-positron-ion magnetoplasma

Theoretical and numerical studies are performed for the nonlinear structures (explosive, solitons, and shock) in quantum electron-positron-ion magnetoplasmas. For this purpose, the reductive perturbation method is employed to the quantum hydrodynamical equations and the Poisson equation, obtaining extended quantum Zakharov–Kuznetsov equation. The latter has been solved using the generalized expansion method to obtain a set of analytical solutions, which reflects the possibility of the propagation of various nonlinear structures. The relevance of the present investigation to the white dwarfs is highlighted.

Nyquist Method for Wigner-Poisson Quantum Plasmas

By means of the Nyquist method, we investigate the linear stability of electrostatic waves in homogeneous equilibria of quantum plasmas described by the Wigner-Poisson system. We show that, unlike the classical Vlasov-Poisson system, the Wigner-Poisson case does not necessarily possess a Penrose functional determining its linear stability properties. The Nyquist method is then applied to a two-stream distribution, for which we obtain an exact, necessary and sufficient condition for linear stability, as well as to a bump-in-tail equilibrium.

Quantum Ion-Acoustic Waves

The one-dimensional two-species quantum hydrodynamic model is considered in the limit of small mass ratio of the charge carriers. Closure is obtained by adopting an equation of state pertaining to a zero-temperature Fermi gas for the electrons and by disregarding pressure effects for the ions. By an appropriate rescaling of the variables, a nondimensional parameter H, proportional to quantum diffraction effects, is identified. The system is then shown to support linear waves, which in the limit of small H resemble the classical ion-acoustic waves. In the weakly nonlinear limit, the quantum plasma is shown to support waves described by a deformed Korteweg–de Vries equation which depends in a nontrivial way on the quantum parameter H. In the fully nonlinear regime, the system also admits traveling waves which can exhibit periodic patterns. The quasineutral limit of the system is also discussed. ©2003 American Institute of Physics. @DOI: 10.1063/1.1609446 #

Stability Analysis of a Three-Stream Quantum-Plasma Equilibrium

We apply the Nyquist method to analyze the stability of small amplitude electrostatic waves in quantum plasmas described by the Wigner-Poisson system. The technique is presented in detail to assess the stability of a threestream equilibrium distribution function. The topology of the Nyquist diagrams is substantially changed with increasing quantum diffraction effects.

Variational approach for the quantum Zakharov system

The quantum Zakharov system is described in terms of a Lagrangian formalism. A time-dependent Gaussian trial function approach for the envelope electric field and the low-frequency part of the density fluctuation leads to a coupled, nonlinear system of ordinary differential equations. In the semiclassical case, linear stability analysis of this dynamical system shows a destabilizing role played by quantum effects. Arbitrary values of the quantum effects are also considered, yielding the ultimate destruction of the localized, Gaussian trial solution. Numerical simulations are shown for both the semiclassical and the full quantum cases.

Breather mode in the many-electron dynamics of semiconductor quantum wells

We demonstrate the existence of a breather mode in the self-consistent electron dynamics of a semiconductor quantum well. A nonperturbative variational method based on quantum hydrodynamics is used to determine the salient features of the electron breather mode. Numerical simulations of the time-dependent Wigner-Poisson or Hartree equations are shown to be in excellent agreement with our analytical results. For asymmetric quantum wells, a signature of the breather mode is observed in the dipole response, which can be detected by standard optical means.

Relativistic Klein-Gordon-Maxwell multistream model for quantum plasmas.

A multistream model for spinless electrons in a relativistic quantum plasma is introduced by means of a suitable fluidlike version of the Klein-Gordon-Maxwell system. The one- and two-stream cases are treated in detail. A new linear instability condition for two-stream quantum plasmas is obtained, generalizing the previously known nonrelativistic results. In both the one- and two-stream cases, steady-state solutions reduce the model to a set of coupled nonlinear ordinary differential equations, which can be numerically solved, yielding a manifold of nonlinear periodic and soliton structures. The validity conditions for the applicability of the model are addressed.

On the generalized Hamiltonian structure of 3D dynamical systems

Abstract The Poisson structures for 3D systems possessing one constant of motion can always be constructed from the solution of a linear PDE. When two constants of motion are available the problem reduces to a quadrature and the structure functions include an arbitrary function of them.