The current understanding of some important nonlinear collective processes in quantum plasmas with degenerate electrons is presented. After reviewing the basic properties of quantum plasmas, model equations (e.g., the quantum hydrodynamic and effective nonlinear Schrodinger-Poisson equations) are presented that describe collective nonlinear phenomena at nanoscales. The effects of the electron degeneracy arise due to Heisenberg’s uncertainty principle and Pauli’s exclusion principle for overlapping electron wave functions that result in tunneling of electrons and the electron degeneracy pressure. Since electrons are Fermions (spin-1/2 quantum particles), there also appears an electron spin current and a spin force acting on electrons due to the Bohr magnetization. The quantum effects produce new aspects of electrostatic (ES) and electromagnetic (EM) waves in a quantum plasma that are summarized in here. Furthermore, nonlinear features of ES ion waves and electron plasma oscillations are discussed, as well as the trapping of intense EM waves in quantum electron-density cavities. Specifically, simulation studies of the coupled nonlinear Schrodinger and Poisson equations reveal the formation and dynamics of localized ES structures at nanoscales in a quantum plasma. The effect of an external magnetic field on the plasma wave spectra and develop quantum magnetohydrodynamic equations are also discussed. The results are useful for understanding numerous collective phenomena in quantum plasmas, such as those in compact astrophysical objects (e.g., the cores of white dwarf stars and giant planets), as well as in plasma-assisted nanotechnology (e.g., quantum diodes, quantum free-electron lasers, nanophotonics and nanoplasmonics, metallic nanostructures, thin metal films, semiconductor quantum wells, and quantum dots, etc.), and in the next generation of intense laser-solid density plasma interaction experiments relevant for fast ignition in inertial confinement fusion schemes.

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Colloquium : nonlinear collective interactions in quantum plasmas with degenerate electron fluids

Under certain circumstances, three or more interacting particles may form bound states. Although the general few-body problem is not analytically solvable, the so-called Efimov trimers appear for a system of three particles with resonant two-body interactions. The binding energies of these trimers are predicted to be universally connected to each other, independent of the microscopic details of the interaction. By exploiting a Feshbach resonance to widely tune the interactions between trapped ultracold lithium atoms, we find evidence for two universally connected Efimov trimers and their associated four-body bound states. A total of 11 precisely determined three- and four-body features are found in the inelastic-loss spectrum. Their relative locations on either side of the resonance agree well with universal theory, whereas a systematic deviation from universality is found when comparing features across the resonance.

Universality in Three- and Four-Body Bound States of Ultracold Atoms

https://aip.scitation.org/doi/pdf/10.1016/j.mre.2016.10.002

Review of quantum collision dynamics in Debye plasmas

Hot, dense plasmas exhibit screened Coulomb interactions, resulting from the collective effects of correlated many-particle interactions. In the lowest particle correlation order (pair-wise correlations), the interaction between charged plasma particles reduces to the Debye-Huckel (Yukawa-type) potential, characterized by the Debye screening length D. Due to the importance of Coulomb interaction screening in dense laboratory and astrophysical plasmas, hundreds of theoretical investigations have been carried out in the past few decades on the plasma screening effects on the electronic structure of atoms and their collision processes employing the Debye-Huckel screening model. The present article aims at providing a comprehensive review of the recent studies in atomic physics in Debye plasmas. Specifically, the work on atomic electronic structure, photon excitation and ionization, electron/positron impact excitation and ionization, and excitation, ionization and charge transfer of ion-atom/ion collisions will be reviewed.

A review of quantum collision dynamics in Debye plasmas

Ground-state energies and wavefunctions for helium atom (He) in exponential-cosine-screened Coulomb potentials (ECSCP) with screening parameter λ, have been obtained for various values of λ within the framework of Ritz's variational principle. Highly correlated and extensive wavefunctions have been used to obtain energy eigenvalues. The ground-state energies of He for various values of λ have been shown to converge with the increase of the terms in the wavefunction. The ground-state energies of He+ along with the ionization potentials of He have also been reported. Our present work represents a first calculation, for the first time in the literature, of the ground-state energies of He interacting with ECSCP.

https://iopscience.iop.org/article/10.1088/0953-4075/42/7/075002/pdf

Ground states of helium in exponential-cosine-screened Coulomb potentials

We have made an investigation on the $2{s}^{2}\text{ }{^{1}S}^{e}$ resonances in helium (He) in exponential cosine-screened Coulomb potentials (ECSCP). Highly correlated wave functions are used to take into account of the correlation effect of the charged particles. Resonance energies and widths for the doubly excited He in ECSCP are determined using the stabilization method by calculating the density of the resonance states. Results for resonance energies and widths are reported for the screening parameter in the range 0.0--0.275

Doubly excited resonance states of helium in exponential cosine-screened Coulomb potentials

We have made an investigation on the ground states and the 2s21Se resonance states of H− in dense quantum plasmas. Exponential-cosine-screened Coulomb potentials (ECSCP) are used to represent the effective potential for a test charge in dense quantum plasmas. Ground-state energies and wavefunctions are determined within the framework of Ritz's variational principle by employing highly correlated wavefunctions to take into account the correlation effect of the charged particles. Ground-state energies are shown to converge with the increase of terms in the wavefunctions. We also report various expectation values of the coordinates of electrons in H−. Resonance energies and widths for the doubly excited H− for various values of the screening parameter are determined using the stabilization method by calculating the density of the resonance states. Results for resonance energies and widths are reported for the screening parameter in the range 0.0–0.15. Such a calculation for H− is reported for the first time in the literature.

https://iopscience.iop.org/article/10.1088/0953-4075/42/17/175006/pdf

Ground states and doubly excited resonance states of H - embedded in dense quantum plasmas

Scattering of positrons from the ground state of hydrogen atoms embedded in dense quantum plasma has been investigated by applying a formulation of the three-body collision problem in the form of coupled multi-channel two-body Lippmann-Schwinger equations. The interactions among the charged particles in dense quantum plasma have been represented by exponential cosine-screened Coulomb potentials. Variationally determined hydrogenic wave function has been employed to calculate the partial-wave scattering amplitude. Plasma screening effects on various possible mode of fragmentation of the system e++H(1s) during the collision, such as 1s→1s and 2s→2s elastic collisions, 1s→2s excitation, positronium formation, elastic proton-positronium collisions, have been reported in the energy range 13.6-350 eV. Furthermore, a comparison has been made on the plasma screening effect of a dense quantum plasma with that of a weakly coupled plasma for which the plasma screening effect has been represented by the Debye model. ...

Positron scattering from hydrogen atom embedded in dense quantum plasma

We have made an investigation to study the plasma screening effect of dense quantum plasmas on the photodetachment cross section of hydrogen negative ion within the framework of dipole approximation. Plasma screening effect has been taken care of by the exponential cosine-screened Coulomb potential (ECSCP). The asymptotic forms of highly correlated wave functions for the initial bound states of ${\text{H}}^{\ensuremath{-}}$ and the plane wave form for the final ${e}^{\ensuremath{-}}\ensuremath{-}\text{H}$ states are used to evaluate the transition matrix elements. Results for photodetachment cross section in dense quantum plasmas are reported for the plasma screening parameter in the range [0.0,0.6] (in ${a}_{0}^{\ensuremath{-}1}$). In respect of the photodetachment process of ${\text{H}}^{\ensuremath{-}}$, we have also compared the plasma screening effect of a dense quantum plasma with that of a weakly coupled plasma for which plasma screening effect has been represented by the Debye model. Our results for the unscreened case agree nicely with some of the most accurate results available in the literature.

Arijit Ghoshal

Papers

Ground states of helium in exponential-cosine-screened Coulomb potentials

Doubly excited resonance states of helium in exponential cosine-screened Coulomb potentials

Ground states and doubly excited resonance states of H - embedded in dense quantum plasmas

Positron scattering from hydrogen atom embedded in dense quantum plasma

Photodetachment of H- in dense quantum plasmas.