Abstract:
The formation of dust ion-acoustic shocks (DIASs) in a four-component quantum plasma whose constituents are electrons, both positive and negative ions and immobile charged dust grains, is studied. The effects of both the dissipation due to kinematic viscosity and the dispersion caused by the charge separation as well as the quantum tunneling due to the Bohm potential are taken into account. The propagation of small but finite amplitude dust ion-acoustic waves (DIAWs) is governed by the Korteweg-de Vries-Burger (KdVB) equation which exhibits both oscillatory and monotonic shocks depending not only on the viscosity parameters, but also on the quantum parameter H (the ratio of the electron plasmon to the electron Fermi energy) and the positive to negative ion density ratio. Large amplitude stationary shocks are recovered for a Mach number exceeding its critical value. Unlike the small amplitude shocks, quite a smaller value of the viscosity parameter, H and the density ratio may lead to the large amplitude monotonic shock strucutres. The results could be of importance in astrophysical and laser produced plasmas.

Abstract:
The nonlinear propagation of dust-acoustic (DA) waves in a magnetized dusty plasma with a pair of trapped ions is investigated. Starting from a set of hydrodynamic equations for massive dust fluids as well as kinetic Vlasov equations for ions, and applying the reductive perturbation technique, a Korteweg-de Vries (KdV)-like equation with a complex coefficient of nonlinearity is derived, which governs the evolution of small-amplitude DA waves in plasmas. The complex coefficient arises due to vortex-like distributions of both positive and negative ions. An analytical as well as numerical solution of the KdV equation are obtained and analyzed with the effects of external magnetic field, the dust pressure as well as different mass and temperatures of positive and negative ions.

Abstract:
The propagation of surface electromagnetic waves along a uniform magnetic field is studied in a quantum electron-hole semiconductor plasma. A new forward propagating mode, not reported before, is found by the effect of quantum tunneling, which otherwise does not exist. In the classical limit ($\hbar\rightarrow 0$) one of the low-frequency modes is found similar to an experimentally observed one in $n$-type InSb at room temperature. The surface modes are shown to be significantly modified in the case of high-conductivity semiconductor plasmas where electrons and holes may be degenerate. The effects of the external magnetic field and the quantum tunneling on the surface wave modes are discussed.

Abstract:
We study the amplitude modulation of low-frequency, long-wavelength electrostatic drift-wave envelopes in a nonuniform quantum magnetoplasma consisting of cold ions and degenerate electrons. The effects of tunneling associated with the quantum Bohm potential and the Fermi pressure for nonrelativistic degenerate electrons, as well as the equilibrium density and magnetic field inhomogeneities are taken into account. Starting from a set of quantum magnetohydrodynamic (QMHD) equations, we derive a nonlinear Schr\"odinger equation (NLSE) that governs the dynamics of the modulated quantum drift-wave packets. The NLSE is used to study the modulational instability (MI) of a Stoke's wave train to a small plane wave perturbation. It is shown that the quantum tunneling effect as well as the scale length of inhomogeneity play crucial roles for the MI of the drift-wave packets. Thus, the latter can propagate in the form of bright and dark envelope solitons or as drift-wave rogons in degenerate dense magnetoplasmas.

Abstract:
The nonlinear theory of dust-acoustic waves (DAWs) with Landau damping is studied in an unmagnetized dusty negative-ion plasma in the extreme conditions when the free electrons are absent. The cold massive charged dusts are described by fluid equations, whereas the two-species of ions (positive and negative) are described by the kinetic Vlasov equations. A Korteweg de-Vries (KdV) equation with Landau damping, governing the dynamics of weakly nonlinear and weakly dispersive DAWs, is derived following Ott and Sudan [Phys. Fluids {\bf 12}, 2388 (1969)]. It is shown that for some typical laboratory and space plasmas, the Landau damping (and the nonlinear) effects are more pronounced than the finite Debye length (dispersive) effects for which the KdV soliton theory is not applicable to DAWs in dusty pair-ion plasmas. The properties of the linear phase velocity, solitary wave amplitudes (in presence and absence of the Landau damping) as well as the Landau damping rate are studied with the effects of the positive ion to dust density ratio $(\mu_{pd})$ as well as the ratios of positive to negative ion temperatures $(\sigma)$ and masses $(m)$.

Abstract:
The formation of small but finite amplitude electrostatic shocks in the propagation of quantum ion-acoustic waves (QIAWs) obliquely to an external magnetic field is reported in a quantum electron-positron-ion (e-p-i) plasma. Such shocks are seen to have double-layer (DL) structures composed of the compressive and accompanying rarefactive slow-wave fronts. Existence of such DL shocks depends critically on the quantum coupling parameter $H$ associated with the Bohm potential and the positron to electron density ratio $\delta$. The profiles may, however, steepen initially and reach a steady state with a number of solitary waves in front of the shocks. Such novel DL shocks could be a good candidate for particle acceleration in intense laser-solid density plasma interaction experiments as well as in compact astrophysical objects, e.g., magnetized white dwarfs.

Abstract:
We consider here chiral symmetry breaking in quantum chromodynamics arising from gluon condensates in vacuum. Through coherent states of gluons simulating a mean field type of approximation, we show that the off-shell gluon condensates of vacuum generate a mass-like contribution for the quarks, giving rise to chiral symmetry breaking. We next note that spontaneous breaking of global chiral symmetry links the four component quark field operator to the pion wave function. This in turn yields many hadronic properties in the light quark sector in agreement with experiments, leading to the conclusion that low energy hadron properties are primarily driven by the vacuum structure of quantum chromodynamics.

Abstract:
We investigate the propagation characteristics of electrostatic waves in a magnetized pair-ion plasma with immobile charged dusts. It is shown that obliquely propagating (OP) low-frequency (in comparison with the negative-ion cyclotron frequency) long-wavelength "slow" and "fast" modes can propagate, respectively, as dust ion-acoustic (DIA) and dust ion-cyclotron (DIC)-like waves. The properties of these modes are studied with the effects of obliqueness of propagation $(\theta)$, the static magnetic field, the ratios of the negative to positive ion masses $(m)$ and temperatures $(T)$ as well as the dust to negative-ion number density ratio $(\delta)$. Using the standard reductive perturbation technique, we derive a Korteweg-de Vries (KdV) equation which governs the evolution of small-amplitude OP DIA waves. It is found that the KdV equation admits only rarefactive solitons in plasmas with $m$ well below its critical value $m_c~(\gg1)$ which typically depends on $T$ and $\delta$. It is shown that the nonlinear coefficient of the KdV equation vanishes at $m=m_c$, i.e., for plasmas with much heavier negative ions, and the evolution of the DIA waves is then described by a modified KdV (mKdV) equation. The latter is shown to have only compressive soliton solution. The properties of both the KdV and mKdV solitons are studied with the system parameters as above, and possible applications of our results to laboratory and space plasmas are briefly discussed.

Abstract:
The nonlinear propagation of electrostatic dust-acoustic (DA) waves in a magnetized dusty plasma consisting of negatively charged mobile dusts, nonthermal fast electrons and trapped ions with vortex-like distribution is studied. Using the reductive perturbation technique, a Korteweg-de Vries (KdV)-like equation is derived which governs the dynamics of the small-amplitude solitary waves in a magnetized dusty nonthermal plasma. It is found that due to the dust thermal pressure, there exists a critical value $(\beta_c)$ of the nothermal parameter $\beta~(>1)$, denoting the percentage of energetic electrons, below which the DA solitary waves cease to propagate. The soliton solution (travelling wave) of the KdV-like equation is obtained, and is shown to be only of the rarefactive type. The properties of the solitons are analyzed numerically with the system parameters. It is also seen that the effect of the static magnetic field (which only modifies the soliton width) becomes significant when the dust gyrofrequency is smaller than one-tenth of the dust plasma frequency. Furthermore, the amplitude of the soliton is found to increase (decrease) when the ratio of the free to trapped ion temperatures $(\sigma)$ is positive (negative). The effects of the system parameters including the obliqueness of propagation $(l_z)$ and $\sigma$ on the dynamics of the DA solitons are also discussed numerically, and it is found that the soliton structures can withstand perturbations and turbulence during a considerable time. The results should be useful for understanding the nonlinear propagation of DA solitary waves in laboratory and space plasmas (e.g., Earth's magnetosphere, auroral region, heliospheric environments etc.).

Abstract:
The effects of linear Landau damping on the nonlinear propagation of dust-acoustic solitary waves (DASWs) are studied in a collisionless unmagnetized dusty plasma with two species of positive ions. The extremely massive, micron-seized, cold and negatively charged dust particles are described by fluid equations, whereas the two species of positive ions, namely the cold (heavy) and hot (light) ions are described by the kinetic Vlasov equations. Following Ott and Sudan [Phys. Fluids {\bf 12}, 2388 (1969)], and by considering lower and higher-order perturbations, the evolution of DASWs with Landau damping is shown to be governed by Korteweg-de Vries (KdV), modified KdV (mKdV) or Gardner (KdV-mKdV)-like equations. The properties of the phase velocity and the Landau damping rate of DASWs are studied for different values of the ratios of the temperatures $(\sigma)$ and the number densities $(\mu)$ of hot and cold ions as well the cold to hot ion mass ratio $m$. The distinctive features of the decay rates of the amplitudes of the KdV, mKdV and Gardner solitons with a small effect of Landau damping are also studied in different parameter regimes. It is found that the Gardner soliton points to lower wave amplitudes than the KdV and mKdV solitons. The results may be useful for understanding the localization of solitary pulses and associated wave damping (collisionless) in laboratory and space plasmas (e.g., the F-ring of Saturn) in which the number density of free electrons is much smaller than that of ions and the heavy, micron seized dust grains are highly charged.