Quantum Hydrodynamic Model Research Articles

Nonlinear Langmuir oscillations in an ultrarelativistic degenerate quantum electron-ion plasma

The investigation of the nonlinear Langmuir associations in an ultrarelativistic, fully degenerate quantum plasma, composed of stationary ions and warm electrons is considered. The quantum hydrodynamic model with the equation of state of electrons is used to derive a nonlinear differential equation that describes the chemical potential of electrons. Then, the Runge Kutta method is used to solve this equation numerically. Hence, the profiles of the chemical potential and electron number density are graphically presented. Numerical results show that the Bohm quantum force produces small scale quantum Langmuir oscillations along with the classical oscillations. These findings are helpful in understanding the features of nonlinear Langmuir waves in various astrophysical plasmas such as planetary interiors and compact objects.

Existence of solutions for a viscous hybrid quantum system for arbitrary large current density

In this paper, we continue to analyse the properties of the hybrid model introduced in the works by Chiarelli et al. and Di Michele et al. In particular, we consider a quantum hybrid model with a special viscous functional, as introduced in the work by Gamba and Jüngel, for the quantum hydrodynamical model in its standard form (QHD). We show that the hybrid QHD (H-QHD) model admits weak solutions also for arbitrary large value of the current density J under a suitable pressure function.

Chiral Berry plasmon dispersion of the two-dimensional electron gas based on a quantum hydrodynamic model

We employ the quantum hydrodynamic model to investigate the properties of chiral Berry plasmons (CBPs) generated by a high-density two-dimensional electron gas (2DEG) film covering a semi-infinite dielectric substrate with a finite Berry flux. By coupling Maxwell's equations, Poisson's equation, and the boundary conditions, we derive the dispersion relations of plasmon with a nonzero Berry flux in detail. We present the difference in the dispersion of CBPs with quantum effects and the classical model. We show how the quantum effect, Berry curvature, the dielectric constant of the substrate, and electron density in 2DEG affect the behavior of the CBPs. Parameter dependence of the effects is calculated and discussed.

Laser induced electron drift in the magnetized quantum plasma: electron spin effects

The spin effect on accumulation of the electron density profile in the presence of an external magnetic field is investigated. In this regard, the two-fluid quantum hydrodynamic model is used to derive the interaction of intense laser light with magnetized quantum plasma. The results emphasize that the initial laser intensity and external magnetic field play significant roles in the accumulation of electron density. Moreover, the behavior of spin-up and spin-down electrons in the same spatial position is completely different. In a way, where spin-up electrons accumulate, spin-down electron density is rarefied. This fact provides a useful recipe for spintronics applications.

Two stream instabilities in unmagnetized nonrelativistic quantum plasma

The objective of this study is to analyse instabilities and growth rate in unmagnetized dense non-relativistic collisionless quantum plasma under the impact of dynamics of ions. Model of quantum hydrodynamics is used to observe the streaming instabilities in highly dense inhomogeneous unmagnetized quantum plasma at low temperature. The model includes continuity and momentum equations for degenerate electrons and nondegenerate ions which interact with each other due to electrostatic field. Using normal mode analysis and linearization, perturbed potential is obtained in terms of unperturbed parameters with the help of first order perturbation in densities and velocities of electrons and ions while neglecting higher order perturbations. Variation in growth rates for detected instabilities is observed by using appropriate quantum plasma parameters.

Stationary Structures in a Four Component Dense Magnetoplasma With Lateral Perturbations

We considered a dense plasma containing electrons, positrons, ions and dust particles in background magnetic and gravitational fields alongside collisional effects for the heavier species (ions and dust particles). Such plasmas are found in magnetars, black hole accretion disks, and so on. The quantum hydrodynamic (QHD) model was used to construct the governing equations of the plasma. Relativistic degeneracy pressure is taken as the equation of state for the electrons and positrons. Effects of exchange-correlation potential were also considered for the lighter species. We employed the reductive perturbation method (RPM) in order to obtain the Zakharov–Kuznetsov (ZK) equation describing 3-D ion acoustic waves (IAWs) with minimal lateral perturbations. Low order analytical solutions allow us to understand the parametric dependence of said structures. Our newly developed numerical technique: homotopy assisted symbolic simulation (HASS) sheds light on the gradual evolution of higher order stationary formations in the system. The results thus obtained can potentially explain certain astrophysical phenomena as well as dense laboratory plasmas.

Resonant Interactions and Chaotic Excitation in Nonlinear Surface Waves in Dense Plasma

By employing a quantum hydrodynamic (QHD) model with appropriate boundary conditions, the nonlinear self-interaction of an electrostatic surface wave on otherwise homogeneous semibounded plasma with degeneracy effects is investigated. It has been found that a part of the second harmonic generated through self-interaction does not have a true surface wave feature but propagates obliquely away from the plasma–vacuum interface into the bulk of the plasma. Such a situation is obtained in laser–plasma interaction during surface etching, plasma processing, and so on. In this article, we study the harmonics generation mechanism, associated Lagrangian chaos, and harmonic conversation rate when an intense laser is incident on an unmagnetized plasma. The dense plasma displays quantum diffraction effects and other quantum statistical effects. We made use of perturbative analysis for the field quantities. The findings will help workers dealing with laser–plasma interaction so as to enhance the tendency of harmonic generation and energy localization.

Bifurcation Analysis of EAWs in Degenerate Astrophysical Plasma: Chaos and Multistability

Bifurcation analysis and dynamical system studies are carried out to find the stability regime and chaotic scenario in electron acoustic waves in relativistic degenerate plasma. We have obtained the quantum hydrodynamic model and obtain the Korteweg–de Vries equation describing the nature and characteristics of solitary structures. The amplitude modulated envelop soliton formation due to external perturbations has been studied by analyzing the nonlinear Schrodinger equation. Further to study the stability factors and the parametric range for such stability, the dynamical system is studied and bifurcation analysis has been carried out. The chaotic behavior of the system is studied through largest Lyapunov exponent (LLE). This work will find application in theoretically predicting the stable modes in many solar plasma and stellar plasma applications and in laser plasma in future.

Drifts effect on the ordinary plasma wave and the existence of new spin dependent electron drift in the spin quantum plasma

Using a separated spin evolution quantum hydrodynamic model, we have derived generalized formula for drift effects of electrons in the inhomogeneous and nonuniform magnetized spin quantum plasma. We report, for the first time, the appearance of new spin dependent drift along with grad-B drift and diamagnetic drift. These results can be used to study the drift effects on various waves and instabilities. To check the applicability of our results, we have derived the dispersion relation of ordinary-mode (O-mode) incorporating electron spin, gradient in density, and magnetic field. We have studied various new features due to electron spin, perpendicular spin drifts, and grad B on the propagation of O-mode. Numerical analysis is presented for the choice of laboratory plasma parameters.

Rogue Wave Generation Through Nonlinear Self-Interaction of Electrostatic Waves in Dense Plasma

In this work, we start with the quantum hydrodynamic model equations for two temperature-populated electrons in a dense plasma with quantum effects. We obtain the KdV equation for the electron acoustic (EAW) mode. The EAW self-interacts to form a rogue wave-type envelop soliton which is described by the nonlinear Schrodinger (NLS) equation. To study the stability criteria, we transform the KdV and NLS equations into its dynamical system counterparts and analyze the phase portraits and carry out the bifurcation analysis. The possibility of hyperchaos is discussed with reference to rogue waves. The finding will be helpful in laser plasma interactions, microelectronics, as well as beam plasma physics and fusion technology.

Blowup of smooth solutions to the isentropic compressible quantum hydrodynamic model

In this article, we consider the blowup phenomenon of smooth solutions to the isentropic compressible quantum hydrodynamic model (QHD) with the initial density of compact support in arbitrary space dimensions.

Quantum corrections on threshold and growth rate of modulational amplification in semiconductor magneto-plasmas

Using the quantum hydrodynamic model (QHDM), quantum corrections (via Bohm potential) on modulational amplification characteristics in semiconductor magneto-plasmas are investigated. Expressions are obtained for the threshold pump amplitude and the growth rate of the modulated beam with including and excluding quantum effects (QEs). Numerical analysis is performed for [Formula: see text]-InSb/CO2 laser system. The dependence of the threshold pump amplitude and the growth rate of the modulated beam on wave number, applied magnetic field (via cyclotron frequency), and plasma carrier concentration (via plasma frequency) are explored. The lowering in threshold pump amplitude and enhancement of growth rate of the modulated beam is observed by incorporating the QEs. The analysis provides detailed information of QEs on semiconductor magneto-plasmas and establishes the technological potentiality of semiconductor magneto-plasmas as the hosts for the fabrication of efficient optical modulators.

The arbitrary amplitude of a solitary pulse propagating obliquely in electron spin‐polarized plasma

AbstractA Separated Spin Evolution Quantum Hydrodynamics Model is employed to investigate arbitrary amplitude ion‐acoustic waves in magnetized plasma, which consists of inertia‐less degenerated electrons with spin‐up and spin‐down states, as well as inertial classical ions. In a two‐dimensional plasma geometry, a homogeneous magnetic field is assumed to be directed along the z‐axis, that is, . In the linear analysis, two branches of waves propagation are found to occur in the oblique direction. The characteristics of large‐amplitude ions solitary waves propagation in oblique direction are studied through an energy‐balance equation, by applying a Sagdeev potential approach. The parametric role of the spin density polarization ratio on the properties of solitary wave structures, as well as other important plasma parameters, is traced analytically. The scope of our work is significant to study dilute magnetic semiconductors, magnetosphere, and as well as astrophysical systems.

The effect of nonideal boundary condition on instability of THz plasma waves in quantum field-effect transistors

The instability of THz plasma waves propagating along a channel of field-effect transistors opens up a new mechanism of emission of THz waves. In this work, we investigate the instability of THz plasma waves in field-effect transistors in the presence of quantum effects and nonideal boundary condition at the source and the drain by using the quantum hydrodynamic model. The results show that the THz plasma waves will be unstable when the gate–source capacitances are larger than gate–drain capacitances and the instability increment can be increased by increasing gate–source capacitances or decreasing gate–drain capacitances. The results of this work give nano-field-effect transistors an advantage in achieving real THz oscillations.

Shocks and solitons in collisional dense laser produced plasmas

The characteristics of nonlinear electron-acoustic waves such as shocks and solitons, are investigated in a three component, dense laser produced plasma consisting of ions and two distinct groups of electrons, using the quantum hydrodynamic model and the standard reductive perturbation method. The modified Korteweg-deVries (mKdV) and Korteweg-deVries-Burgers (KdVB) equations have been derived for the electron-acoustic waves in the plasma. The dependence of both shocks and solitons on various parameters has been extensively studied. It is observed that whenever the density crosses the limit from the classical to the quantum range, the effective potential remains invariant for the solitary profiles; but shows a slight variation for the shock profiles. The collisional effect plays a significant role in the dissipation of solitary waves and the dissipation is larger for higher values of collision frequencies. The results obtained could prove helpful for understanding the parametric dependence of nonlinear waves in highly intense laser plasma interactions.

Shock physics in warm dense matter: A quantum hydrodynamics perspective

AbstractWarm dense matter (WDM), an exotic, highly compressed state of matter between solid and plasma phases, is of high current interest, in particular for astrophysics and inertial confinement fusion. For the latter, in particular the propagation of compression shocks is crucial. The main unknown in the shock propagation in WDM is the behaviour of the electrons since they are governed by correlations, quantum and spin effects that need to be accounted for simultaneously. Here we describe the shock dynamics of the warm dense electron gas using a quantum hydrodynamic model. From the numerical hydrodynamic simulations, we observe that the quantum Bohm pressure induces shear force that weakens the formation and strength of the shock. In addition, the Bohm pressure induces an electron density response that takes the form of oscillations. This is confirmed by the theoretical analysis of the early stage of the shock formation. Our theoretical and numerical analyses allow us to identify characteristic dimensionless shock propagation parameters at which the effect of the Bohm force is important.

Applications of Solvable Lie Algebras to a Class of Third Order Equations

A family of third-order partial differential equations (PDEs) is analyzed. This family broadens out well-known PDEs such as the Korteweg-de Vries equation, the Gardner equation, and the Burgers equation, which model many real-world phenomena. Furthermore, several macroscopic models for semiconductors considering quantum effects—for example, models for the transmission of electrical lines and quantum hydrodynamic models—are governed by third-order PDEs of this family. For this family, all point symmetries have been derived. These symmetries are used to determine group-invariant solutions from three-dimensional solvable subgroups of the complete symmetry group, which allow us to reduce the given PDE to a first-order nonlinear ordinary differential equation (ODE). Finally, exact solutions are obtained by solving the first-order nonlinear ODEs or by taking into account the Type-II hidden symmetries that appear in the reduced second-order ODEs.

Effect of Viscosity on Stopping Power for a Charged Particle Moving above Two-Dimensional Electron Gas

In two-dimensional (2D) electron systems, the viscous flow is dominant when electron-electron collisions occur more frequently than the impurity or phonon scattering. In this work, a quantum hydrodynamic model, considering viscosity, is proposed to investigate the interaction of a charged particle moving above the two-dimensional viscous electron gas. The stopping power, perturbed electron gas density, and the spatial distribution of the velocity vector field have been theoretically analyzed and numerically calculated. The calculation results show that viscosity affects the spatial distribution and amplitude of the velocity field. The stopping power, which is an essential quantity for describing the interactions of ions with the 2D electron gas, is calculated, indicating that the incident particle will suffer less energy loss due to the weakening of the dynamic electron polarization and induced electric field in 2D electron gas with the viscosity. The values of the stopping power may be more accurate after considering the effect of viscosity. Our results may open up new possibilities to control the interaction of ions with 2D electron gas in the surface of metal or semiconductor heterostructure by variation of the viscosity.

Grey solitons in the ultracold fermions at the full spin polarization

A minimal coupling quantum hydrodynamic model of spin-1/2 fermions at the full spin polarization corresponding to a nonlinear Schrodinger equation is considered. The nonlinearity is primarily caused by the Fermi pressure. It provides an effective repulsion between fermions. However, there is the additional contribution of the short-range interaction appearing in the third order by the interaction radius. It leads to the modification of the pressure contribution. Solitons are considered for the infinite medium with no restriction on the amplitude of the wave. The Fermi pressure leads to the soliton in form of the area of decreased concentration. However, the center of solution corresponding to the area of minimal concentration has nonzero value of concentration. Therefore, the grey soliton is found. Soliton exist if the speed of its propagation is below the Fermi velocity. Keywords: degenerate fermions, hydrodynamics, non-linear Schrodinger equation, dark soliton, Fermi pressure.

Cold Fusion Based on Matter-Antimatter Plasma Formed in Molecular Crystals

The main purpose of this work is to shed light on the possibility of producing huge amount of energy based on the construction matter-antimatter plasma in a molecular crystal. It is assumed that two beams of isothermal hydrogen and antihydrogen are injected into a palladium crystal leading to a plasma state composed of particles and antiparticles. The collapse of this state releases a huge amount of energy which can be used as fuel for space shuttles. Thus, the novel system of isothermal pressure interaction enhances the energy power carried out by the quantum ion acoustic soliton (QIAS). In addition to the energy power released from the particle-antiparticle annihilation. The probability of merging the energy from these two cases is available at certain condition. The released energy may be a significant step in solving the energy scape of Tokomak to produce fusion energy. The study starting from the one-dimensional quantum hydrodynamic model (in which the term of electron-positron and proton-antiproton for hydrogen-antihydrogen is included), a Korteweg de Vries equation (kdv) is derived, the QIAS energy experiences and the annihilation energy power are calculated. It is found that the total energy of QIAS and the energy resulting from hydrogen-antihydrogen annihilation are important step towards the establishment of a cold fusion power station.