The dynamics of a tridimensional, axially degenerated vibration coupled to a finite Fermi system shaped as a cylindrical reservoir in the Markovian–plus–weak-coupling regime is investigated. The vibration is aimed at representing a normal mode of the fermion system and is extracted out of a hydrodynamical construction for the relative motion of a two-fluid mixture. Such a procedure provides a dispersion relation that has been proven to work properly in nuclear theory. A residual coupling between the mode and the heat reservoir constituted by the single-particle degrees of freedom is adopted and equations of irreversible evolution for the oscillator components and for the fermionic population can be obtained. This dynamical system is numerically integrated for a variety of container sizes and particle numbers and it is shown that thermodynamic magnitudes characterizing the attractor of the dynamical system, as well as typical relaxation times, can be consistently extracted from the numerical approach.

The quantum-mechanical system whose potential is the cusp catastrophe is studied. The qualitative features of this system, including the eigenvalue spectrum, density of states, wave-function localization and delocalization, probability distribution, operator expectation values, and matrix elements, are studied as functions of the cusp control parameter values. Canonical features preceding and accompanying the transition from the single-mode to the double-mode regime have been determined. The relationships between the qualitative properties of the quantum cusp and the canonical properties of the cusp catastrophes are exhibited.

A differential-equation method to obtain the exact solutions to the functional renormalization-group fixed-point equation, the deterministic eigenvalue equation, and the stochastic eigenvalue equation for intermittency is introduced. Application of the method to the one-dimensional case is explained in detail, and the generalization to two and higher dimensions is immediate.

It is pointed out that for boosts and rotations on orthogonal axes, a factorization of the product of their characters is possible. By using this theorem on factorization, one can factor the nontrivial products of representations in the homogeneous Lorentz group. The method is used to derive some well-known and some new formulas which define the parameters of the Thomas, or Wigner, rotation.

We evaluate the exact propagator for the time-dependent three-dimensional charged harmonic oscillator in a time-varying magnetic field. We show that such a propagator can be obtained from that for a charged particle in a constant magnetic field.

In this work we discuss the problems underlying the time evolution of states driven by SU(2) and SU(1,1) coherence-preserving Hamiltonians, using the Wei-Norman algebraic procedure. We also solve the problem of finding the explicit time evolution of a quantum system whose Hamiltonian is a time-dependent linear combination of the SU(1,1) group generators and those of the Weyl-Heisenberg algebra. The relevance of this Hamiltonian to the generation of antibunched radiation in a laser-plasma scattering experiment is also briefly analyzed.

The bound-state energies of the generalized exponential-cosine screened Coulomb potential are determined by using the method of large-N expansion. The results for the exponential-cosine screened Coulomb potential are then immediately obtained as a special case. It is shown that the 1/N expansion technique yields the same analytic perturbation series for the energies as obtained by employing the hypervirial equations with the Hellmann-Feynman theorem.

Various separations, or ‘‘gauge choices,’’ are possible for the decomposition of the total Hamiltonian into electronic and internuclear terms. We show that, for one particular choice, all long-range Coulomb terms are associated with the internuclear motion. The potential then associated with electronic transitions is non-Coulombic. Some practical consequences of this gauge choice are discussed.

Enhanced Doppler coverage has been observed in the laser-induced optical pumping of low-density rubidium vapor in the absence of any buffer gas. Transient and steady-state measurements show that this enhancement arises from velocity-changing collisions (VCC’s) of rubidium atoms with the walls of the cell containing the vapor. Wall-induced VCC’s offer a possible mechanism for increasing the efficiency with which atomic and nuclear polarization may be produced with lasers.

Systematic measurements of K${\alpha }_2$ to K${\alpha }_1$ intensity ratios have been carried out for a wide range of targets with 62≤Z≤82 using 3.5-MeV protons. The total uncertainty in the measured values is mostly less than 0.5%. All the results agree with Scofield’s calculations within the uncertainty.

We report what we believe to be the first observation of a laser-induced fluorescence band, excited by absorption from a low-lying state of the ${\mathrm{Hg}}_3$ excimer using a ‘‘pump-and-probe’’ method. A study of the fluorescence intensity as a function of the time separation between the ‘‘pump’’ and ‘‘probe’’ laser pulses provides clear evidence for the presence of both ${\mathrm{Hg}}_3$ and ${\mathrm{Hg}}_2$ molecules in the laser-excited mercury vapor. The fluorescence may be due to trimer emission or to dimer emission following dissociation of a trimer state.

We present a proof that there are no zeros in the nonrelativistic Coulomb dipole matrix elements, considered as functions of energy, for transitions between any bound state and states of greater energy. This includes bound-bound and bound-free transitions and also transitions to unbounded negative energy states. Our result follows from the recursion relations for dipole matrix elements obtained by Infeld and Hall. By contrast, zeros occur in some Coulomb quadrupole matrix elements.

We have observed a chemical-environment effect on the total K x-ray yield of sulfur in ${\mathrm{SF}}_6$, ${\mathrm{SO}}_2$, and ${\mathrm{H}}_2$S. The yield from ${\mathrm{SF}}_6$ is 16% higher than the yield from ${\mathrm{H}}_2$S, whereas the yield from ${\mathrm{SO}}_2$ is, within error, the same as ${\mathrm{H}}_2$S. Variation in the fluorescence yield for the different molecules is considered to be the most probable cause of the effect.

We study a quantum model in which transitions occur between structureless continua. The population is in one of the continua initially. When the continuum-continuum coupling is very strong, we show that the continua are decoupled and population trapping occurs.

Energy-loss straggling of ions with v≪$v_F$ in an electron gas has been evaluated from phase shifts determined from nonlinear, density-functional calculations. These results differ markedly from those obtained from linear theory and show oscillations in straggling with increasing nuclear charge which can be correlated with the scattering properties of electrons at the Fermi level.

Some of the differences among several alternative formulations of constant-pressure molecular dynamics are described. The formulations all agree in the large-system limit, but differ for small systems.

The use of combinatorial algebra for understanding diffusive motion on a geometrically ordered fractal lattice is demonstrated. The specific example of the fractal lattices used are the Pascal-Sierpiński gaskets of prime orders of which the well-known Sierpiński gasket is a special case. It is shown that the conclusions obtained from such an analysis can be meaningfully interpreted in physical terms.

Using the mapping of classical and spatially continuous diffusion onto a quantum system, we establish the connection between long-time diffusive behavior and the leading low-frequency properties in the density of states. The mapping also relates the hitherto independent fields of classical diffusion in random media and localization. Moreover, the approach is extended to spatially discrete diffusion. Here, the low-frequency scaling behavior is connected to intermittency in one-dimensional maps and confirmed by numerical results for a model exhibiting sublinear diffusion.

A simple model is proposed that allows an efficient storage and retrieval of random patterns. Also correlated patterns can be handled. The data are stored in an Ising-spin system with ferromagnetic interactions between all the spins and the main idea is to ‘‘chop’’ the system along the boundaries where the patterns differ.

We report results of extensive modified-hypernetted-chain calculations for a model fluid-argon–solid-${\mathrm{CO}}_2$ interface by employing a nonlocal ansatz for the inhomogeneous bridge function. For a given bulk density, the system is found to approach complete wetting for values of the temperature, and of the substrate-fluid coupling parameter, which are in good agreement with density-functional-theory estimates. The calculations also show the presence of a ‘‘surface spinodal line,’’ which is briefly illustrated.