Variational approach for the quantum Zakharov system

Haas, Fernando

doi:10.1063/1.2722271

Cited by 51 publications

(39 citation statements)

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“…However, the system can be decoupled in the adiabatic as well as semiclassical limit [2,6], where the solitons can be found to be more stable than in fully degenerate cases [6]. Other recent developments on the QZEs can be found in the literature [3][4][5][6][7][9][10][11]. Marklund [3] studied the kinetic theory of LWs interacting with quantum ionacoustic waves (QIAWs), where it was shown that the combined effects of partial coherence and quantum correction tend to enhance the modulational instability (MI) growth rate [3].…”

Section: Introductionmentioning

confidence: 99%

“…Marklund [3] studied the kinetic theory of LWs interacting with quantum ionacoustic waves (QIAWs), where it was shown that the combined effects of partial coherence and quantum correction tend to enhance the modulational instability (MI) growth rate [3]. The temporal dynamics of the QZEs has been studied by Haas by means of a variational approach [4]. It has been found that the quantum coupling parameter plays a destabilizing role on localized structures, or Langmuir wave packets.…”

Section: Introductionmentioning

confidence: 99%

“…Refs. [3][4][5][6]) indicate that much attention has been paid to investigate the dynamics of such one-dimensional (1D) QZEs. Very recently, a more comprehensive work on the dynamics of LWs has been studied by Haas and Shukla in a threedimensional quantum Zakharov system [7].…”

Section: Introductionmentioning

confidence: 99%

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Temporal dynamics in the one-dimensional quantum Zakharov equations for plasmas

et al. 2010

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The temporal dynamics of the quantum Zakharov equations (QZEs) in one spatial dimension, which describes the nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs) is revisited by considering their solution as a superposition of three interacting wave modes in Fourier space. Previous results in the literature are modified and rectified. Periodic, chaotic as well as hyperchaotic behaviors of the Fourier-mode amplitudes are identified by the analysis of Lyapunov exponent spectra and the power spectrum. The periodic route to chaos is explained through an one-parameter bifurcation analysis. The system is shown to be destabilized via a supercritical Hopf-bifurcation. The adiabatic limits of the fully spatio-temporal and reduced systems are compared from the viewpoint of integrability properties.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Temporal dynamics in the one-dimensional quantum Zakharov equations for plasmas

et al. 2010

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“…Some astrophysical compact objects, such as white dwarf or neutron stars, possess very high temperature but strong quantum effects as well due to their large densities (∼ 10 6 g/cm 3 ) [6]. There has been recent studies in quantum plasmas involving quantum turbulence [7], quantum analogues for the Harris sheet [8], quantum models taking into account spin [9,10], stable solitary structures [11], dark soliton and vortices solutions [12], variational structures for the quantum Zakharov system [13] as well as application of quantum hydrodynamic equations for carbon nanotubes [14].…”

Section: Introductionmentioning

confidence: 99%

Macroscopic description for the quantum Weibel instability

Haas

Lazar

2008

Phys. Rev. E

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The Weibel instability in the quantum plasma case is treated by means of a fluid-like (moments) approach. Quantum modifications to the macroscopic equations are then identified as effects of first or second kind. Quantum effects of the first kind correspond to a dispersive term, similar to the Bohm potential in the quantum hydrodynamic equations for plasmas. Effects of the second kind are due to the Fermi statistics of the charge carriers and can become the dominant influence for strong degeneracy. The macroscopic dispersion relations are of higher order than those for the classical Weibel instability. This corresponds to the presence of a cutoff wave-number even for the strong temperature anisotropy case.

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“…Hass [23], Misra and Samanta [24], Mistra et al [25] etc. However, these investigations are based on the electron equation of state valid for the nonrelativistic limit.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Propagation of Dust-Ion-Acoustic Waves in a Degenerate Dense Plasma

Zobaer¹,

Roy²,

Mamun³

2012

JMP

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Nonlinear propagation of dust-ion-acoustic waves in a degenerate dense plasma (with the constituents being degenerate, for both the limits non-relativistic or ultra-relativistic) have been investigated by the reductive perturbation method. The Korteweg de-Vries (K-dV) equation and Burger's equation have been derived, and the numerical solutions of those equations have been analyzed to identify the basic features of electrostatic solitary and shock structures that may form in such a degenerate dense plasma. The implications of our results in compact astrophysical objects, particularly, in white dwarfs, have been briefly discussed.Keywords: Degenerate Plasma; Dust-Ion-Acoustic Waves; K-dV Equation; Burzer's EquationIn present days, most theoretical concerns are to understand the environment of the compact objects having their interiors supporting themselves via degenerate pressure. The degenerate pressure, which arises due to the combine effect of Pauli's exclusion principle (Wolfgang Ernst Pauli, 1925) and Heisenberg's uncertainty principle (Werner Heisenberg, 1927), depends only on the fermion number density, but not on it's temperature. This degenerate pressure has a vital role to study the electrostatic perturbation in matters existing in extreme conditions [1][2][3][4][5][6][7]. The extreme conditions of matter are caused by significant compression of the interstellar medium. High density of degenerate matter in these compact objects (which are, in fact, "relics of stars") is one of these extreme conditions. These interstellar compact objects, having ceased burning thermonuclear fuel and thereby no longer generate thermal pressure, are contracted significantly, and as a result, the density of their interiors becomes extremely high to provide non-thermal pressure through degenerate pressure of their constituent particles and particle-particle interaction. The observational evidence and theoretical analysis imply that these compact objects support themselves against gravitational collapse by degenerate pressure.The degenerate electron number density in such a compact object is so high (e.g. in white dwarfs it can be of the order of 10 30 cm −3, even more [8]) that the electron Fermi energy is comparable to the electron mass energy and the electron speed is comparable to the speed of light in vacuum. The equation of state for degenerate electrons in such interstellar compact objects are mathematically explained by Chandrasekhar [4] for two limits, namely non-relativistic and ultra-relativistic limits. The interstellar compact objects provide us cosmic laboratories for studying the properties of the medium (matter), as well as waves and instabilities [9][10][11][12][13][14][15][16][17][18][19][20][21][22] in such a medium at extremely high densities (degenerate state) for which quantum as well as relativistic effects become important [9,21]. The quantum effects on linear [16,18,22] and nonlinear [17,20] propagation of electrostatic and electromagnetic waves have been investigated by using the quantum hyd...

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Variational approach for the quantum Zakharov system

Cited by 51 publications

References 29 publications

Temporal dynamics in the one-dimensional quantum Zakharov equations for plasmas

Temporal dynamics in the one-dimensional quantum Zakharov equations for plasmas

Macroscopic description for the quantum Weibel instability

Nonlinear Propagation of Dust-Ion-Acoustic Waves in a Degenerate Dense Plasma

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