Quantum Bohm Potential Research Articles

Nonlinear excitation of wakefields in quantum plasma channel

A detailed analytical study for wakefields excitation in a channel of quantum plasma is presented. The recently developed quantum hydrodynamic (QHD) model has been used to develop the interaction picture. Applying the perturbations in the laser fields orders, the magnetic and electric wakefields have been obtained for a Gaussian laser pulse. The electrons trapped by the wakefields are accelerated to extremely high energies. The quantum effects of Fermi statistical pressure and the quantum Bohm potential have been found to make significant changes in the nature of wakefields generated. The plasma channel helps in self-focusing and also contributes to acceleration. Both the longitudinal and transverse forces acting on the accelerating electron have been calculated.

The Hubble tension from the standpoint of quantum cosmology

The Hubble tension is analyzed in the framework of quantum cosmological approach. It is found that there arises a new summand in the expression for the total energy density stipulated by the quantum Bohm potential. This additional energy density acts similarly to a stiff matter component, modifying the expansion history of the early universe and decaying with scale factor a as a-6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a^{-6}$$\\end{document}, faster than radiation, in late universe. Taking account of this matter-energy component of quantum nature can, in principle, eliminate a discrepancy between the direct late time model-independent measurements of the Hubble constant and its indirect model dependent estimates. The considered model allows one to extend the standard cosmology to quantum sector.

Propagatory dynamics of electromagnetic drift waves in inhomogeneous spin degenerate compact objects plasmas

A theoretical analysis is carried out to investigate the dynamics of electromagnetic drift modes in non-uniform spin quantum magnetoplasmas found in degenerate compact objects. General dispersion relations are derived using spin quantum hydrodynamic equations, Poisson equation, and Maxwell equation, with and without ion inertial effects. The effects of quantum spin magnetization, Bohm potential, and density inhomogeneity on the dispersion of electromagnetic drift modes are explored numerically. The advancing theoretical analysis demonstrated herein has strong correlations and consistencies with the dynamic growth of compact astrophysical objects and their surrounding atmospheres, such as black holes, white dwarfs, and dense molecular clouds.

Ponderomotive effects in spin—polarized quantum plasma

Analysis of ponderomotive effects exciting from propagation of an intense laser pulse through high density quantum plasma under the influence of an axial magnetic field taking into consideration the spin–spin (up and down) exchange interaction. The effects of electron Fermi pressure, quantum Bohm potential, and electron spin have been included in the analysis. Spin polarization is a result of the concentration difference of opposite spin electrons which is produced under the influence of the applied magnetic field. Axial gradient of the ponderomotive potential of laser has been applied for the electron acceleration. An analytic solution of the electron energy gain is obtained and the influence of spin polarization is analyzed both numerically and analytically. It is observed that spin polarization, density perturbation and the magnetic field effect electron acceleration dramatically. Further, the effect of nonlinearity on the refractive index of plasma has been studied.

Effect of spin polarization on electron acceleration in magnetized quantum plasma by a surface plasma wave.

The effect of spin-up and spin-down exchange interaction on electron acceleration by a surface plasma wave (SPW) propagating in magnetized quantum plasma has been studied. The SPW was excited over the metal-vacuum interface with maximum amplitude at the interface. The effective dielectric constant was evaluated, considering the effects of quantum Bohm potential, degenerate Fermi pressure, and electron spin. The externally applied magnetic field perturbed the densities of the oppositely spinning electrons, which resulted in spin polarization. The dispersion relation and energy exchange mechanism for the electron acceleration was built, incorporating the effects of spin polarization in the wave-plasma interaction. The energy gain was found to increase with the spin polarization.

Effect of spin-polarization on filamentation in magnetized quantum plasma

A theoretical study analysing the effects of spin- polarization resulting from the difference in concentration of the oppositely spinning electrons on the filamentation instability of an intense laser beam propagating in magnetized quantum plasma. The ponderomotive force has been evaluated taking into account the electron’s Fermi pressure, quantum Bohm potential and electron’s spin. The effective dielectric constant has been calculated. For the filamentaton instability, the dispersion relation has been established and the growth rate has been studied analytically. The spin-polarization is found to enhance the filamentation.

Global weak solution to the degenerate quantum Navier‐Stokes‐Maxwell equations with damping term

AbstractIn this paper we investigate the global existence of the finite energy weak solution to the isentropic quantum Navier‐Stokes‐Maxwell equations with density‐dependent viscosity and the damping term in three‐dimensional periodic domain. This model is composed of the isentropic compressible Navier‐Stokes‐Maxwell equation with density‐dependent viscosity, the quantum Bohm potential and a damping term. This model can be used to describe the motion of the particle in the plasma under the electric–magnetic field. The main techniques are the Faedo‐Galerkin method, some imbedding inequalities and some compactness theorems.

Laser beam guiding in partially stripped magnetized quantum plasma

Relativistic and ponderomotive nonlinearities arising by the passage of a linearly polarized laser beam through a partially stripped magnetized quantum plasma are analyzed. The interaction formalism has been developed using the recently developed quantum hydrodynamic model. The effects associated with the Fermi pressure, quantum Bohm potential and electron spin have been incorporated. A nonparaxial, non-linear wave equation has been obtained by the use of source dependent expansion technique and spot size has been evaluated. The nonlinear relativistic self-focusing tends to focus the beam while the ponderomotive nonlinearity tends to defocus. The effect of magnetization and quantum effects on the spot size and the beam power have been studied.

Zero absolute vorticity plane Couette flow as an hydrodynamic representation of quantum energy states under perpendicular magnetic field

Here we extend the Madelung transformation of the Schrödinger equation into a fluid-like form to include the influence of an external electromagnetic field on a charged particle. The vorticity of the Madelung fluid is then in the opposite direction to the imposed magnetic field and equal in magnitude to the cyclotron angular frequency. When the particle motion is confined to a plane, perpendicular to an imposed magnetic field, the equivalent flow dynamics is that of zero absolute vorticity obtained in a quasi-two-dimensional rotating frame, where the cyclotron frequency plays a role equivalent to that of the Coriolis frequency in a rotating frame. We show how the Landau levels and the extended modes in the integer quantum Hall effect are all mapped into such zero absolute vorticity-like plane Couette flows, where the latter exhibit a geostrophic-like balance between the magnetic force and the gradients of the quantum (Bohm) potential and the electric force.

Probing quantum effects with classical stochastic analogs

We propose a method to construct a classical analog of an open quantum system, namely a single quantum particle confined in a potential well and immersed in a thermal bath. The classical analog is made out of a collection of identical wells where classical particles of mass $m$ are trapped. The distribution $n(x,t)$ of the classical positions is used to reconstruct the quantum Bohm potential $V_{\rm Bohm} = -\frac{\hbar^2}{2 m} \frac{\Delta \sqrt{n}}{\sqrt{n}}$, which in turn acts on the shape of the potential wells. As a result, the classical particles experience an effective "quantum" force. This protocol is tested with numerical simulations using single- and double-well potentials, evidencing typical quantum effects such as long-lasting correlations and quantum tunneling. For harmonic confinement, the analogy is implemented experimentally using micron-sized dielectric beads optically trapped by a laser beam.

Spin contribution to the instability of THz plasma waves

When the boundary conditions of the source and drain are asymmetric, the plasma waves may become unstable in the channel of a field effect transistor (FET). We use the quantum magnetohydrodynamic model to study the influence of the quantum Bohm potential, Fermi statistical pressure, and electron spin effects on the stability of THz plasma waves propagating perpendicular to the magnetic field in the FET. A dispersion equation governing the THz plasma oscillation is obtained. Numerical results have shown that the presence of spin effects has enlarged the instable range of β, enhanced the instability increment, and made the frequency of THz plasma waves larger. The research shows that nanometer FETs with spin effects have advantages in realizing practical terahertz radiation.

Nonlinear coupling of upper-hybrid waves with lower-hybrid waves in a degenerate dense plasma

The nonlinear coupling of high-frequency upper-hybrid (UH) pump waves with low-frequency lower-hybrid (LH) waves is studied in a degenerate magnetoplasma, comprising of quantum electrons and classical ions. For this purpose, the framework of quantum hydrodynamic model is utilized to examine the Fermi pressure effects on the nonlinear dispersion relations of UH and LH waves with quantum settings. Furthermore, by applying the Fourier analysis and collecting the same phasor terms, the nonlinear dispersion relations can be coupled to investigate the growth rates of three-wave decay and modulational instabilities under certain approximations. It is noticed that inclusion of electron Fermi pressure significantly alters the parametric three-wave decay and modulational instabilities besides the corrections due to quantum exchange-correlations and Bohm potential in degenerate magnetoplasmas. The present findings might be useful to understand the nonlinear wave interactions in superdense astrophysical environments, e.g., white dwarfs, magnetars, neutron stars, etc.

Quantum hydrodynamic theory of quantum fluctuations in dipolar Bose–Einstein condensate

Traditional quantum hydrodynamics of Bose-Einstein condensates (BECs) is restricted by the continuity and Euler equations. The quantum Bohm potential (the quantum part of the momentum flux) has a nontrivial part that can evolve under quantum fluctuations. The quantum fluctuations are the effect of the appearance of particles in the excited states during the evolution of BEC mainly consisting of the particles in the quantum state with the lowest energy. To cover this phenomenon in terms of hydrodynamic methods, we need to derive equations for the momentum flux and the current of the momentum flux. The current of the momentum flux evolution equation contains the interaction leading to the quantum fluctuations. In the dipolar BECs, we deal with the long-range interaction. Its contribution is proportional to the average macroscopic potential of the dipole-dipole interaction (DDI) appearing in the mean-field regime. The current of the momentum flux evolution equation contains the third derivative of this potential. It is responsible for the dipolar part of quantum fluctuations. Higher derivatives correspond to the small scale contributions of the DDI. The quantum fluctuations lead to the existence of the second wave solution. The quantum fluctuations introduce the instability of the BECs. If the dipole-dipole interaction is attractive, but being smaller than the repulsive short-range interaction presented by the first interaction constant, there is the long-wavelength instability. There is a more complex picture for the repulsive DDI. There is the small area with the long-wavelength instability that transits into a stability interval where two waves exist.

High-frequency surface waves in quantum plasmas with electrons relativistic degenerate and exchange-correlation effects

The propagation characteristics of high-frequency surface waves are studied in spin-1/2 quantum plasmas by considering the electron relativistic degenerate and exchange-correlation effects. Using the quantum fluid equations of magnetoplasmas in the presence of the quantum Bohm potential, spin magnetization energy, relativistic degenerate pressure, and exchange-correlation effects, a generalized dispersion relation is derived. The analytical and numerical results show that the relativistic degenerate and exchange-correlation effects significantly modify the propagation properties of high-frequency surface waves. It is found that under the influence of exchange-correlation effects, the frequency spectrum of high-frequency surface waves will be down-shifted. It is also indicated that the dispersion curve shifts up with the increase of relativistic gamma factor. Furthermore, the phase speed of the high-frequency surface waves increases with increasing electron number density. The current research is helpful to understand the propagation of the high-frequency surface waves in quantum plasmas, such as those in dense astrophysical environment.

Boundary graphene layer effect on surface plasmon oscillations in a quantum plasma half-space

The effect of graphene on unique features of surface plasmon-polariton excitations near the interface of vacuum and quantum plasma half-space is explored using a quantum hydrodynamic model including the Fermi electron temperature and the quantum Bohm potential together with the full set of Maxwell equations. It is found that graphene as a conductive layer significantly modifies the propagation properties of surface waves by making a change on the corresponding wave dispersion relation. It is shown that the presence of graphene layer on the interface of vacuum and plasma leads to a blue-shift in the surface Plasmon frequency. The results of present study must be contributed to the modern electronic investigations.

Propagation of surface waves in semi-bounded quantum collisional plasmas with electron exchange-correlation effects

The propagation of surface waves in semi-bounded quantum collisional plasmas are investigated by taking into account the quantum Bohm potential, Fermi statistical pressure, electron exchange-correlation effects and collisional effects. The modified quantum hydrodynamic model in conjunction with Maxwell equations are used to obtain the new general dispersion relations of surface waves, and the dispersion relations are discussed in some special cases of interest. It is indicated that the wave frequency spectrum can be down-shifted due to the electron exchange-correlation effects. It is also shown that the growth rate of surface waves instability can be enhanced by increasing the collisional frequency, especially in the short wavelength region. The corresponding results can be helpful for identifying surface waves which transport in intense metallic plasmas.

Skyrmion–electron interaction in the separated spin-up and spin-down quantum hydrodynamics approach

Abstract The Berry gauge field associated with adiabatic quantum evolution represents a very interesting area of research, especially for the description of non-relativistic fermions coupled to a skyrmion texture. We construct a quantum hydrodynamics model that describes the electron–skyrmion interactions, with separate descriptions of spin-up and spin-down electrons as two different fluids. The quantum effects, represented by the quantum Bohm potential, are taken into account. We investigate the electron gas moving in a smooth magnetic texture, where the magnetic moments adjust to the local magnetization direction of the skyrmion, and derive the equations of motion and evolution of spin density for two fluids of electrons in the emergent gauge fields. Applying the separated spin evolution quantum hydrodynamics to the 2D electron gas, traveling on the background of the Berry gauge field in plane samples, located in an external magnetic field, we predict a wave of a new kind in the electron gas. This novel wave appears as an influence of emergent fields and quantum effects.

Electrostatic Langmuir waves and spin-electron-acoustic waves in spin polarized plasma double layer

The quantum hydrodynamic model for the electrostatic wave in the two parallel layers of two dimensional electron gases is developed. It is considered for two regimes: classic regime and quantum regime with the separate spin evolution. There are two Langmuir-like waves in the classic regime. Their frequency (ω) dependencies have an interferencelike pattern on concentrations ω2∼(n01+n02 ± 2n01n02), where 01 and n02 are the equilibrium concentrations of the electrons in each layer of electron gas and ± refers to the spectrum of two waves. This spectrum appears instead of the couple of Langmuir waves in two noninteracting two-dimensional electron gases. In the quantum regime, the separate spin evolution leads to the spectrum of four waves instead of the two Langmuir waves present in two noninteracting two-dimensional electron gases. Two extra waves are related to the separate spin evolution of electrons. They are associated with the spin-electron acoustic waves. The contribution of the quantum Bohm potential has also been considered. The influence of the concentrations of electrons, the interlayer distance, and the spin polarization on the spectrum of waves is studied numerically.

Conversion efficiency of even harmonics of whistler pulse in quantum magnetoplasma

AbstractStudy of even harmonic generation resulting from propagation of whistler pulse in homogeneous high-density quantum plasma immersed in an externally applied magnetic field, using the recently developed quantum hydrodynamic model is presented. The effects of quantum Bohm potential, quantum statistical pressure, and electron spin have been taken into account. The field amplitude of even harmonic of the whistler with respect to fundamental wave and the conversion efficiency for phase-mismatch has been analyzed. The conversion efficiency of harmonic radiation depends on the plasma electron density, magnetic field strength as well as the intensity of whistler pulse. The efficiency increases significantly with an increase in plasma density, magnetic field and whistler wave intensity. Higher conversion efficiency is observed in degenerate plasma for lower values of the static magnetic field as compared with classical plasma.

Oblique propagation of longitudinal spin-electron acoustic waves under the influence of the Coulomb exchange interaction and the quantum Bohm potential

The influence of the exchange interaction on the properties of spin-electron acoustic waves at the oblique propagation of waves relative to the external magnetic field in the magnetically ordered metals is studied. The spectra of the Langmuir wave and the Trivelpiece-Gould wave is also considered. It is well-known that there are two branches of the spectrum of the spin-electron acoustic waves in this regime. The change of their properties under the influence of the exchange interaction is studied. The quantum Bohm potential is included either. The exchange interaction and the quantum Bohm potential give opposite contributions, but they do not compensate each other since they have different dependences on the wave vector. This competition creates a non-monotonical behavior of the Trivelpiece-Gould wave spectrum. The concavity changes in the monotonic spectra of the Langmuir wave and the SEAWs are found.