The study of electron acoustic waves (EAWs) and their associated solitary structures in semiconductor quantum plasma doped with nanoparticle clusters has been carried out. The system consists of cold and hot electrons, holes, and stationary ions. The theory has been built using the quantum hydrodynamic (QHD) model. The dispersion relation for EAWs has been set up. To explore nonlinear behaviour, the perturbation technique has been applied, leading to the Korteweg de Vries (KdV) equation. The analysis demonstrates that quantum effects stabilize wave propagation at higher frequencies, while the presence of nanoparticles strongly influence wave dispersion at higher frequencies. Nonlinear analysis shows that solitons in quantum plasma attain higher amplitudes and broader structures due to quantum effects and with the inclusion of nanoparticles.

A Kappa distribution function applicable to systems comprising mixed fermions and bosons has been developed through the thermodynamic Gibbs potential, utilizing the quantum versions of Olbert's Kappa distributions. The generalized expressions of the partition function and the entropy have been evaluated for such mixed quantum systems. The analysis shows that boson-rich systems consistently exhibit higher entropy than fermion-rich systems. The distribution functions show heavy-tailed characteristics at low Kappa index values, indicating the presence of superthermal particles. It is observed that relativistic effects lead to a significant increase in entropy.

This work presents a study of the coupling between lattice ion vibrations and electron waves in magnetized piezoelectric semiconductor quantum plasmas using the quantum hydrodynamic (QHD) model. A quantum modified dispersion relation has been derived, incorporating the quantum corrections and external magnetic field. A set of nonlinear evolution equations has been established through the application of the two-time scale theory, and a soliton solution for these coupled nonlinear evolution equations has been obtained using the modified quantum Zakharov equations. The obtained solitons exhibit cusp-like solitary structures, characterized by sharp, non-differentiable peaks. The findings reveal that the amplitude of the soliton field increases significantly with particle density, while it decreases with the strength of the magnetic field and piezoelectric coupling coefficient. Inclusion of exchange and correlation potential enhances localization, producing sharper soliton profiles. These findings demonstrate that magnetic field and quantum effects provide effective control over soliton dynamics and wave transmission.

The propagation of an electrostatic wave in a three-component e-p-I astrophysical quantum plasma in a rotating frame has been studied, taking into account the particle spin, Fermi pressure, and quantum Bohm potential. Spin polarization plays a key role in explaining the dynamics of quantum plasmas, especially in astrophysical contexts due to the high external magnetic field prevalent in such environments. Effects specific to this particular environment, like rotation as well as gravity, have also been included. Coupled dispersion of electron, positron, and ion modes has been obtained. Further, the investigation of solitary waves by the Korteweg de Vries method has been carried out, and a soliton solution has been obtained. Quantum effects increase wave dispersion and soliton stability in quantum plasma, thereby affecting the electrostatic potential.

Electron-acoustic solitary waves (EASWs) in quantum plasma comprising stationary ions, cold electrons, hot electrons, and kappa-distributed electrons have been investigated. The generalized Kappa-Fermi distribution has been modified to include electrostatic energy contribution, and the density of Kappa electrons has been obtained using this modified distribution. Utilizing the quantum hydrodynamic (QHD) model, a dispersion relation has been derived for linear EAWs. Employing the standard reductive perturbation technique, a Korteweg-de Vries (KdV) equation governing the dynamics of EAWs has been derived. The quantum mechanical effects of different parameters like the kappa index, Mach number and equilibrium kappa electron density have been examined on the profiles of EASWs. It is found that the presence of kappa electrons in quantum plasma leads to new results, including steeper dispersion curves, sharper and more localized solitary waves with kappa index and stronger plasma interactions with increased kappa electron density in dense astrophysical environments

Second harmonic generation due to the effect of two different spin states of electron on the propagation of a circularly polarized laser pulse in homogenous high density quantum plasma is studied using the quantum hydrodynamic (QHD) model. The effects associated with the Fermi pressure, the Bohm-potential and the electron spin-up and spin-down have been taken in to account. The efficiency of the Second harmonic radiation is derived and the effect of spin polarization on the conversion efficiency has been analyzed.

A study of the dispersion of an electromagnetic wave propagating through a uniform quantum dusty plasma under the influence of a transverse magnetic field using the quantum hydrodynamic (QHD) model and taking into account the quantum Fermi pressure, Bohm potential and electron spin. The spatial trajectories of the particles have been obtained for electrons, ions, and dust particles. The inclusion of dust particles is significant as they introduce additional mass and charge effects. Subsequently, the nonlinear current density, comprising the conventional current density and the magnetization current density due to electron spin, has been established. Further, the dispersion relation for electromagnetic waves in quantum dusty plasma has been analyzed. The effects of electron spin have been studied both numerically and analytically. The magnetization current density is significant as it plays a crucial role in accounting for the magnetic interactions and spin effects within the plasma, further influencing the overall dispersion characteristics. The results indicate the influence of spin in quantum dusty plasma increases dispersion, as spin-particle interaction modifies the plasma's collective behavior by increasing Fermi pressure and enhancing propagation velocity.

Quantum plasmas in astrophysical environments are abundant due to extreme electric, magnetic, and gravitational fields. These plasmas can be most clearly observed in neutron stars, white dwarfs, brown dwarfs, red dwarfs, accretion disks of black holes, pulsars, quasars, and more. This paper examines the propagation of electromagnetic waves in a three-component e-p-i quantum plasma within a rotating frame, considering the particles' spin, Fermi pressure, and quantum Bohm potential. Additionally, effects unique to this specific environment, such as rotation and gravity, are included. The dispersion of electrons, ions, and positrons has been obtained separately, and their coupling has been analyzed to understand the collective behavior. It has been noted that the quantum effects of Fermi pressure and Bohm potential significantly influence particle dynamics.

The effect of spin polarization, induced by the difference in concentration of spin-up and spin-down electrons produced under the influence of a magnetic field, on lattice ion vibrationselectron wave interactions, and the resulting amplification of acoustic waves in spin polarised piezoelectric semiconductor quantum plasma has been studied. The dielectric permittivity of the high-density plasma medium has been evaluated through which the dispersion relation has been set up. The gain coefficient of acoustic waves has been obtained using the modified separate spin evolution quantum hydrodynamic (SSE-QHD) model for piezoelectric semiconductor plasma. The study reveals that quantum effects, including Fermi pressure and quantum Bohm potential, reduce wave frequency while spin polarization increases it. Acoustic gain rises significantly with frequency in the presence of quantum effects. Spin polarization also contributes to a slight increase in acoustic wave amplification.

A new model to study the dynamics of relativistic quantum plasmas using the quantum electrodynamical (QED) approach has been constructed to analyze the quantum effects, relativistic corrections, and electromagnetic interactions. Considering the covariant Lagrangian function and EulerLagrange equation, the equations of motion have been established describing the interaction of strong electromagnetic waves in plasma. These equations of motion constitute a model for the propagation of relativistic laser pulse through high density quantum plasma. Our model specifically takes the effects of four spin and four velocity into account during the interaction process. This model is applicable to high density plasmas in all ranges of electromagnetic fields which includes astrophysical environments, high power laser plasma interactions, etc.

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.