Quantum Hydrodynamic Equations Research Articles

Klein–Gordon Equations, Equations of Relativistic Quantum Hydrodynamics, and Quantum Shocks in Describing Collisions of Atomic Nuclei

Klein–Gordon Equations, Equations of Relativistic Quantum Hydrodynamics, and Quantum Shocks in Describing Collisions of Atomic Nuclei

A Note on Magnetized and Self-Gravitating Dark Matter Halos with Bose-Einstein Condensation

In the present study, we assume a rotating, self-gravitating dark matter which is magnetized under the influence of Bose-Einstein condensation. For the condensate dark matter halos, the non-relativistic Gross-Pitaevskii equation is used and for the hydrodynamical evolution, continuity and modified Euler equation are considered. The modified Maxwell equation is also considered to show the influences of the magnetic field and finite electrical resistivity. We determine the dispersion relation and the Jeans wave number by assuming slight perturbations of the quantum hydrodynamical equations. From the findings, we found that the Jeans wave number depends on quantum potential and rotation. In the absence of resistivity, we observe that the Jeans wave number modifies due to the magnetic field also.

Modulational instability of ion-acoustic waves in a dense quantum plasma

Modulational instability of ion-acoustic (IA) waves is investigated in an unmagnetized quantum plasma by adopting an equation of state for Fermi electron gas. To this end, a basic set of one-dimensional quantum hydrodynamic equations is reduced to a nonlinear Schrödinger equation using the reductive perturbation method. Quantum corrections are described using a nondimensional quantum parameter H proportional to the quantum diffraction parameter. Based on normalized electron temperature and chemical potential, new quantum criteria of modulational instability for IA waves are obtained and analyzed. Moreover, formation of rogue waves due to the modulational instability of IA waves and propagation of modulated IA packets in the form of bright and dark envelope solitons are examined for two different types of astrophysical plasma regions: white dwarf stars and warm dense matter.

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.

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.

Nonlocal Theory of the Photon Gas Evolution Beginning from the Planck Time

Evolution of the photon gas (PG) in the Planck period is considered as a particular case of the physical vacuum (PV) hydrodynamics. Nonlocal quantum hydrodynamic equations are applied for calculation of the photon gas evolution. In general case, PG hydrodynamics contains gravitation in the explicit form. Exact analytical solutions of PG hydrodynamics are obtained. Solutions show the exponential growth of gradient values for internal energy in time and space. In comparison with phenomenological General Relativistic Theory, Nonlocal quantum hydrodynamics (NQH) does not lead to contradictions in all limit cases. Theory of physical vacuum and the theory of photonic gas are related theories. These theoretical (analytical!) results confirm the result of direct observations (Arno Alan Penzias and Robert Woodrow Wilson, Nobel Prize (1978) for their discovery of cosmic microwave background; John C. Mather and George F. Smoot. Nobel Prize (2006) for their discovery of the blackbody form and anisotropy of the cosmic microwave background radiation).

Quantum Hydrodynamics of Spinning Particles in Electromagnetic and Torsion Fields

We develop a many-particle quantum-hydrodynamical model of fermion matter interacting with the external classical electromagnetic and gravitational/inertial and torsion fields. The consistent hydrodynamical formulation is constructed for the many-particle quantum system of Dirac fermions on the basis of the nonrelativistic Pauli-like equation obtained via the Foldy–Wouthuysen transformation. With the help of the Madelung decomposition approach, the explicit relations between the microscopic and macroscopic fluid variables are derived. The closed system of equations of quantum hydrodynamics encompasses the continuity equation, and the dynamical equations of the momentum balance and the spin density evolution. The possible experimental manifestations of the torsion in the dynamics of spin waves is discussed.

On the Characteristics of Magnetosonic Waves in a Spin-Polarized Degenerate Electron–Positron–Ion Plasma

The linear properties of magnetosonic waves are studied by using the separated spin evolution quantum hydrodynamic equations in which each electron and positron are treated as two different fluids. At the perpendicular propagation, we have only one magnetosonic wave which is affected by both spin polarization and concentration of positron. In the case of oblique propagation, we solve dispersion numerically and found that three wave solutions are obtained without taking into account separate spin evolution (SSE), but the oblique propagation with SSE gives five wave solutions, two of them are electron and positron spin-dependent wave solutions and have been reported for the first time. It is noted that the spin polarization and positron concentration reduce the phase velocities of the obliquely propagating spectra. Moreover, it is seen that the obliqueness effect enhances the frequency of all waves. Finally, the comparison with earlier reported results is also presented. For numerical analysis, we choose parameters relevant to astrophysical environments.

Exchange fluid model derived from quantum kinetic theory for plasmas

AbstractStarting from quantum kinetic theory for ideal plasmas with exchange effects, the quantum hydrodynamic equations are derived from 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.

The existence, uniqueness and exponential decay of global solutions in the full quantum hydrodynamic equations for semiconductors

The existence, uniqueness and exponential decay of global solutions in the full quantum hydrodynamic equations for semiconductors

Impact of an External Magnetic Field on Solitary Waves in Quantum Electron–Hole Plasmas of Semiconductors

The propagation of solitary acoustic pulses in magnetized quantum electron–hole plasmas of semiconductors has been studied. The effects of an external magnetic field and quantum terms, including the electrons and holes quantum recoil effects, exchange-correlation force, and the degenerate pressure of charge carriers are considered. Starting from quantum hydrodynamic equations, by using the reductive perturbation method, the Zakharov–Kuznetsov equation is derived. The theoretical model is applied to three types of semiconductors, namely GaAs, GaSb, and InP. It is clear that basic features of solitary acoustic waves are modified significantly by plasma parameters, especially number densities of semiconductors and magnetic field strength. The value of the amplitude and width of solitary waves strongly depends on the type of semiconductors and the propagation angle in a magnetized quantum electron-hole semiconductor plasma. Numerical results reveal that the width of the solitons gets reduced significantly with the increase of the magnetic field intensity while there is no effect on the amplitude of solitary waves. The weakest magnetic field that sets the pulse width to zero belongs to GaAs. Finally, the stability of the pulse soliton solution of the Zakharov–Kuznetsov equation has been discussed, analytically and numerically. The instability growth rate depends on plasma parameters and magnetic field intensity. The present paper can be meaningful in studying non-linear phenomena and instability behaviors in magnetized quantum electron–hole plasmas of semiconductors and the particle and energy transport mechanism in plasma-assisted quantum semiconductor nanodevices.

Modelling quantum aspects of disruption of a white dwarf star by a black hole

We study the final stages of the evolution of a binary system consisted of a black hole and a white dwarf star. We implement the quantum hydrodynamic equations and carry out numerical simulations. As a model of a white dwarf star we consider a zero temperature droplet of attractively interacting degenerate atomic bosons and spin-polarized atomic fermions. Such mixtures are investigated experimentally nowadays. We find that the white dwarf star is stripped off its mass while passing the periastron. Due to nonlinear effects, the accretion disk originated from the white dwarf becomes fragmented and the onset of a quantum turbulence with giant quantized vortices present in the bosonic component of the accretion disk is observed. The binary system ends its life in a spectacular way, revealing quantum features underlying the white dwarf star’s structure. We find a charged mass, falling onto a black hole, could be responsible for recently discovered ultraluminous X-ray bursts. The simulations show that final passage of a white dwarf near a black hole can cause a gamma-ray burst.

Quantum hydrodynamics description of spin-1 Bose–Einstein condensates

We develop a novel model of the magnetized spin-1 Bose–Einstein condensate (BEC) of neutral atoms, using the method of many-particle quantum hydrodynamic (QHD) and propose an original derivation of the system of continual equations. We consider bosons with a spin-spin interaction and a short range interaction in the first order in the interaction radius, on the of basis of the self-consistent field approximation of the QHD equations. We demonstrate that the dynamics of the fluid velocity and magnetization is determined by a nontrivial modification of the Euler and Landau–Lifshitz equation, and show that a nontrivial modification of the spin density evolution equation contains the spin torque effect that arises from the self-interactions between spins of the bosons. The properties of the dispersion spectrum of collective excitations are described. We obtain the new contribution of the self-interaction of spins in the spin wave spectrum together with the influence of an external magnetic field and spin-spin interactions between polarized particles. The anisotropic spin wave instability is predicted.

Nonlinear modulation of quantum electron acoustic waves in a Thomas–Fermi plasma with effects of exchange-correlation

The amplitude modulation of electron acoustic waves (EAWs) is investigated in an unmagnetized four-component quantum plasma containing dynamic cold electron fluid, Thomas–Fermi distributed hot electrons and positrons and immobile ions in presence of exchange-correlation potentials. For this purpose, basic set of quantum hydrodynamic equations is reduced to a nonlinear Schrodinger equation (NLSE) adopting a reductive perturbation technique. The regions of the stable and unstable wave packets are obtained precisely in terms of the intrinsic plasma parameters. It is shown that the NLSE leads to the modulational instability (MI) of EAWs, and the formation of EA rogue waves, which are due to the effects of nonlinearity and dispersion in the propagation of EAWs. The effects of relevant plasma parameters on the MI criterion are numerically investigated. It is also found that the modulated EAW packets can propagate in the form of bright envelope solitons as well as dark envelope solitons. Within the modulational instability region, the dependence of first- and second-order EA rogue wave profiles on the system parameters is discussed.

Time periodic solutions for the non-isentropic compressible quantum hydrodynamic equations with viscosity in R^3

This article concerns the existence and uniqueness of a time periodic solution for the non-isentropic quantum hydrodynamic equations with viscosity. By applying the Leray-Schauder theory, subtle energy estimates and a limiting method, we obtain the existence of time periodic solutions under some smallness assumptions on the time periodic external force in \(\mathbb{R}^3\). The uniqueness can be proved by similar energy estimates. In particular, the quantum effects and the energy equation are taken into account in this paper which play a significant role in the uniform (in the domain R and the positive constant \(\epsilon\)) estimates, especially in the selection of the norm.
 For more information see https://ejde.math.txstate.edu/Volumes/2020/103/abstr.html

Bistability of Bose–Fermi mixtures

We study formation of a Bose–Fermi droplet in realistic experimental setting. We start with a typical experimental arrangement of two atomic species—bosons and fermions in a harmonic axially symmetric confinement. The variational analysis shows that the system exhibits bistability. For weak repulsion between bosons, one of the equilibrium states, smaller in size, spherically symmetric, and with negative energy, corresponds to quantum droplet; the other with always positive energy represents the elongated droplet-like state immersed in the sea of a fermionic cloud. For stronger repulsion between bosons the bifurcation is seized and only the former state is left. Now it represents an elongated object which, for strong enough boson–fermion attraction, gets negative energy. It becomes an excited Bose–Fermi droplet when the trap is released, what is demonstrated by solving the quantum hydrodynamics equations for the Bose–Fermi system. To depict our ideas we consider the 133Cs–6Li mixture under ideal conditions, i.e. we assume no losses.

Quantum hydrodynamics approach for the research of magnetic skyrmions

We propose a new approach of many-particle quantum hydrodynamics to describe a system of interacting magnetic skyrmions in the external fields. The model is based on the description of skyrmions as a fluid of point-like particles. The equations of many-particle quantum hydrodynamics are obtained for a system of skyrmions with induced dipole moments and charges. The dipole–dipole interaction between dipoles and the Coulomb interaction between charges are taken into account. The influence of quantum effects in the form of the Bohm quantum potential is obtained. The contribution of Magnus effect to the dynamics of dipoles current density is predicted. The electron–skyrmion interactions are considered, based on a two-fluid model of quantum hydrodynamics with separate description of spin-up and spin-down electrons on the background of skyrmion lattice. The proposed model can be further used to study the dynamical effects in a system of skyrmions in the external fields.

Dispersion relation of graphene surface plasmon by using a quantum hydrodynamic model

Abstract A quantum hydrodynamic model is used to study the properties of surface plasmon at an interface between a monolayer graphene sheet and a Voigt substrate. The substrate is assumed as a semiconductor that applying an external magnetic field to the structure in the Voigt configuration. The dispersion relations of graphene surface plasmon are obtained analytically by solving Maxwell’s equations and the quantum hydrodynamic equations. It is found that the quantum effects significantly change the properties of graphene surface plasmon and the features of such plasmon are quite different from those in a classical hydrodynamic model. The results also show that the applied magnetic field and the graphene character greatly affect the graphene surface plasmon. Moreover, The plasmon modes exhibit distinctively different behavior for forward and backward propagating directions, which are in contrast to the cases without the quantum effects. In addition, a one-way plasmon mode is found in the lower band region. Parameter dependence of the effects is examined and discussed.

Quantum-Gravity Screening Effect of the Cosmological Constant in the DeSitter Space–Time

Small-amplitude quantum-gravity periodic perturbations of the metric tensor, occurring in sequences of phase-shifted oscillations, are investigated for vacuum conditions and in the context of the manifestly-covariant theory of quantum gravity. The theoretical background is provided by the Hamiltonian representation of the quantum hydrodynamic equations yielding, in turn, quantum modifications of the Einstein field equations. It is shown that in the case of the DeSitter space–time sequences of small-size periodic perturbations with prescribed frequency are actually permitted, each one with its characteristic initial phase. The same perturbations give rise to non-linear modifications of the Einstein field equations in terms of a suitable stochastic-averaged and divergence-free quantum stress-energy tensor. As a result, a quantum-driven screening effect arises which is shown to affect the magnitude of the cosmological constant. Observable features on the DeSitter space–time solution and on the graviton mass estimate are pointed out.

Finslerian geometrization of quantum mechanics in the hydrodynamical representation

We consider a Finslerian type geometrization of the non-relativistic quantum mechanics in its hydrodynamical (Madelung) formulation, by also taking into account the effects of the presence of the electromagnetic fields on the particle motion. In the Madelung representation the Schr\"{o}dinger equation can be reformulated as the classical continuity and Euler equations of classical fluid mechanics in the presence of a quantum potential, representing the quantum hydrodynamical evolution equations. The equation of particle motion can then be obtained from a Lagrangian similar to its classical counterpart. After the reparametrization of the Lagrangian it turns out that the Finsler metric describing the geometric properties of quantum hydrodynamics is a Kropina metric. We present and discuss in detail the metric and the geodesic equations describing the geometric properties of the quantum motion in the presence of electromagnetic fields. As an application of the obtained formalism we consider the Zermelo navigation problem in a quantum hydrodynamical system, whose solution is given by a Kropina metric. The case of the Finsler geometrization of the quantum hydrodynamical motion of spinless particles in the absence of electromagnetic interactions is considered in detail, and the Zermelo navigation problem for this case is also discussed.