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Edge effects in magnetized charged-particle systems are discussed with the help of a multiple-reflection expansion for the Green function. The profiles of the density and the electric current are determined both for the non-degenerate and the highly degenerate case. The asymptotic form of the profiles near the bulk is found to be exponentially decaying in both cases.

A complete set of equilibrium fluctuation formulas for the charge density, the momentum density and the energy density of a magnetized one-component quantum plasma is presented. The derivation is based on the use of equations of motion for Fourier-transformed imaginary-time Green functions. The resulting formulas depend both on the strength and the orientation of the magnetic field. They are a basic ingredient for the derivation of the collective-mode spectrum in the long-wavelength limit. Projection-operator methods are used to establish explicit expressions for the mode frequencies of a magnetized quantum plasma up to second order in the wave number.

The complete set of second-moment sum rules for the correlation functions of arbitrarily high order describing a classical multi-component ionic mixture in equilibrium is derived from the grand-canonical ensemble. The connection of these sum rules with the large-scale behaviour of fluctuations in an ionic mixture is pointed out.

Mode-coupling theory is used to determine the long-time behaviour of the Green-Kubo integrands for the heat conductivity and the diffusion coefficients of an ionic mixture in a magnetic field. It is shown that the presence of several species of particles with a different ratio of charges and masses is a prerequisite for the validity of dissipative magnetohydrodynamics

Instabilities are predicted for absorptive optical bistability in a nonideal Fabry-Perot cavity on the basis of Maxwell-Bloch theory. The authors show that the stability problem of the Maxwell-Bloch equations can be formulated in terms of a Riccati differential equation with boundary conditions. They have integrated this equation numerically. The results crucially depend on the value of the transmission coefficient of the mirrors. For finite values of this quantity they find that the nearest side mode is responsible for two disconnected instability domains in the plane spanned by the output intensity and the medium response time. One of these domains can generate instabilities in the upper and the lower branch of the steady-state curve if the cooperation parameter is sufficiently large. Higher side modes can give rise to positive-slope instabilities as well. From these findings it can be understood why a recent experimental search for instabilities in absorptive optical bistability has led to a negative result. The authors finally demonstrate that the instability spectra of a Fabry-Perot cavity and a so-called equivalent ring cavity differ considerably

The complete set of fluctuation formulae for the partial densities, the pressure and the energy density of a multi-component ionic mixture is derived from equilibrium statistical mechanics. Sum rules for the pair correlation functions are used to write the fluctuation formulae in terms of thermodynamical quantities.

Two competitive convergent kinetic equations for a one-component Coulomb plasma with small plasma parameter epsilon are discussed. It is shown how a Chapman-Enskog scheme can be set up to calculate the heat conductivity and the viscosity. Both kinetic equations are found to yield identical transport coefficients for small epsilon , at least in lowest order of the Chapman-Cowling truncation procedure.

A general class of approximate expressions for the pair correlation function of a classical one-component plasma with small plasma parameter epsilon is discussed. The collision terms which follow from these approximate correlation functions are characterized by effective potentials that differ from the bare Coulomb potential by modulation factors depending on the interparticle distance. It is shown that for small epsilon the transport coefficients are independent of the precise form of the modulation factors.

The generating functions for the collision brackets associated with two alternative convergent kinetic equations are derived for small values of the plasma parameter. It is shown that the first few terms in the asymptotic expansions of these generating functions are identical. Consequently, both kinetic equations give rise to the same transport coefficients in arbitrarily high order of the Chapman-Cowling truncation scheme.

Equilibrium statistical methods are used to derive sum rules for two- and three-particle correlation functions of a multi-component ionic mixture. Some of these rules are general consequences of the electrostatic character of the interaction, whereas others depend on specific thermodynamic properties of the system. The first group of rules follows from the BBGKY hierarchy and a clustering hypothesis for Ursell functions. The sum rules of the second group are obtained by describing the system with the help of a restricted grand-canonical ensemble in which the particle numbers of the various components in the mixture fluctuate under the condition that the total charge in the system remains constant

The long-range asymptotic expression for the multipole expansion of the retarded interatomic dispersion energy is shown to consist of contributions from electric dipole-dipole, dipole-quadrupole and quadrupole-quadrupole interactions, all varying as the inverse seventh power of the interatomic separation. The general expressions for these interactions lead to short-range series expansions which extend results obtained earlier with the help of the Breit hamiltonian.

The multipole expansion of the retarded interatomic dispersion energy is evaluated in the spherical-tensor formalism. The multipole expansion of the electrostatic dispersion energy follows as a special case.

The multipole expansion of the retarded dispersion energy of two atoms in nondegenerate ground states is derived. The result shows that multipoles of different order may give rise to dispersion energies varying in the same way for large interatomic separations.

The inductive and dispersive retarded interaction energies of two ground- state hydrogen atoms described by Dirac theory are derived up to all multipole orders. The results are obtained by evaluation of Feynman diagrams and with the help of dispersion-relation methods. the nonrelativistic and semi-relativistic approximations of the interaction energy are given in a form that shows explicitly the contributions of electron spin.

A dispersion relation technique is used to obtain the retarded dispersion energy of two neutral atoms in nondegenerate ground states. To that end multipole expansions are derived for the electromagnetic form factors occurring in the vertex function that characterizes the interaction of a neutral atom with a pair of photons on the mass shell. The long-range asymptotic expression for the dispersion energy is shown to contain electric and diamagnetic matrix elements in a symmetric way