[en] This is the final report for the project 'Correlations in Confined Quantum Plasmas', NSF-DOE Partnership Grant DE FG02 07ER54946, 8/1/2007 - 7/30/2010. The research was performed in collaboration with a group at Christian Albrechts University (CAU), Kiel, Germany. That collaboration, almost 15 years old, was formalized during the past four years under this NSF-DOE Partnership Grant to support graduate students at the two institutions and to facilitate frequent exchange visits. The research was focused on exploring the frontiers of charged particle physics evolving from new experimental access to unusual states associated with confinement. Particular attention was paid to combined effects of quantum mechanics and confinement. A suite of analytical and numerical tools tailored to the specific inquiry has been developed and employed

[en] The quantum microfield distribution is defined for the electron electric field distribution in a grand canonical ensemble. The definition is general, allowing for description of the distribution at a charged or neutral point and applies for the electron Coulomb field (high frequency microfield) or shielded field (low frequency microfield). By analogy with the Baranger-Mozer cluster expansion for the classical case a cluster expansion for the microfield distribution is defined. The cluster series is resummed to closed form for the case of no interactions, to define a quantum Holtsmark distribution. In this way the problem is reduced to a one-electron calculation. The usual classical result is verified in the limit of z much less than 1; the large and small field behavior is determined for arbitrary degeneracy

[en] The dynamic and static structure factors, and also their pressure derivatives, for dilute and moderately dense gases are studied theoretically and experimentally. The density region of particular interest is that corresponding to the zeroeth and first order terms in a density expansion of the distribution function. For the static structure factor, the lowest order term provides direct information about the intermolecular pair potential, while the next higher term involves both the pair and triplet potentials. The corresponding terms in the expansion of the dynamic structure factor provide information about the two- and three-body dynamics. Theoretical and Monte Carlo calculations are presented, and compared with available data on krypton

[en] A model for the collision rate of an impurity ion in a plasma is formulated by extending a corresponding model for velocity and electric field correlation functions. All dynamical effects of the plasma are represented by its electric field at the impurity, which is then given a simple stochastic description. The simplest example allows complete determination of the collision rate and solution to the associated kinetic equation. (orig.)

[en] Complete text of publication follows. A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g., MD, integral equations, DFT) to describe quantum systems. The classical system has an effective temperature, local chemical potential, and pair interaction that are defined by requiring equivalence of the grand potential and its functional derivatives with respect to the external and pair potentials for the classical and quantum systems. Practical inversion of this mapping for the classical properties is effected via the hypernetted chain approximation, leading to representations as functionals of the quantum pair correlation function (similar in spirit to the approach of Dharma-wardana and Perrot). The parameters of the classical system are determined such that ideal gas, weak coupling RPA, and strong coupling pair limits are preserved. The potential advantages of this approach are discussed. Research supported by NSF/DOE Partnership in Basic Plasma Science Award DE-FG02-07ER54946, and by US DOE Grant DE-SC0002139.

[en] A set of nonlinear Langevin equations for fluctuations of the local conserved densities in a fluid under shear is proposed. These equations are a model for the extension of hydrodynamics to very short wavelengths at liquid densities. The hydrodynamic modes associated with the linearized equations are studied as a function of wave vector and shear rate. The degeneracy of the viscous shear modes is lifted by the shear, and one of these modes combines with the heat mode to form a propagating pair. As an example of nonequilibrium fluctuations, the dynamic structure factor is calculated for several values of frequency and wave vector. At large shear rates one pair of propagating modes becomes unstable at a wavelength of the order of the particle size. This instability is suggested as a possible explanation for a shear-induced disorder-order transition seen in computer simulations. Nonlinear mode-coupling effects are studied elsewhere

[en] This distribution of electric fields at a neutral point is calculated for a weakly coupled one component plasma at arbitrary degeneracy. The electric field distribution is represented in terms of a quantum cluster expansion generalizing the Baranger-Mozer expansion in the classical case. The part of the series due to exchange correlations in the absence of interactions is summed to closed form. The residual part of the series is truncated after the second term, as is appropriate to lowest order in the plasma parameter. The radial distribution function in the two-body cluster integral is evaluated in the random phase (chain approximation). For asymptotically weak degeneracy the Baranger-Mozer microfield distribution (Debye-Huckel approximation) is regained. As the degeneracy is increased at fixed plasma parameter, the peak of the distribution is shifted toward smaller fields

[en] A unified theory of plasma line broadening is obtained from a quantum kinetic equation, paralleling existing results for a classical plasma. The atom-electron interactions are shielded by equilibrium electron correlation functions and a frequency dependent dielectric function. A 'ring' approximation is used to replace the classical plasma parameter expansion, for typical laboratory conditions. Atom-electron correlations are included as well as electron-electron correlations. (author)

[en] A unified field of plasma line broadening is obtained from a quantum kinetic equation, paralleling existing results for a classical plasma. The atom-electron interactions are shielded by equilibrium electron correlation functions and a frequency dependent dielectric function. A 'ring' approximation is used to replace the classical plasma parameter expansion, for typical laboratory conditions. Atom-electron correlations are included as well as electron-electron correlations. (author)

[en] A quantum kinetic theory of time-correlation functions is described in terms of a formally exact closure of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. The theory closely parallels existing treatments of the corresponding classical problem, so that direct comparisons between approximations for classical and quantum systems may be made. As an illustration, the formalism is applied to conditions of low density, but arbitrary degeneracy, and the resulting kinetic equation is shown to reduce to the linearized form of the Uehling-Uhlenbeck equation with the cross section appropriately modified to account for degeneracy. Also, classical approximations suitable for strongly coupled fluids are generalized to the quantum case. The results are applied to evaluation of the electrical conductivity for a two-component plasma in the following paper