A generalized commutation relation of a single-mode oscillator is proposed. Bose-Einstein, Fermi-Dirac, and Greenberg’s infinite statistics are shown to be special cases of this commutation relation. The Fock states, coherent states, and analogs of squeezed coherent states for this commutation relation are constructed. Finally, the quantization of a free infinite-statistics field is discussed using the Umezawa-Takahashi procedure [H. Umezawa and Y. Takahashi, Prog. Theor. Phys. 9, 14 (1953); Nucl. Phys. 51, 193 (1964)].

We numerically investigate in a laboratory frame the evolution of waves on the surface of fluid flowing down a cylinder in the context of a two-dimensional Kuramoto-Sivashinsky equation. The conditions for convective instability of the system are derived. We show that spiral waves emerge when the flow is driven at the inlet with a combination of spiral driving and random noise. In the case of a purely-noise-driven flow, spiral-like structures appear occasionally as short transients while the main pattern is a straight wave. In most cases the flow tends to be irregular.

Temperature propagation in a near-critical fluid sample (${\mathrm{SF}}_6$) is experimentally studied under reduced gravity in space. Onset of phase separation is indicated by the appearance of a spinodal scattering ring. Critical speeding up of temperature equilibration prior to phase separation and markedly slowed-down temperature equilibration during phase separation are observed.

Strong second-harmonic generation is observed from plasmas generated on aluminium and glass. Both redshifts and blueshifts of the frequency spectra were measured, depending on the angle of incidence. Time-resolved measurements reveal maxima of the second harmonic a few picoseconds after the generation of the plasma.

Excess electron states in neon gas are examined using low-energy-electron–atomic-neon scattering data and a simple theoretical model. We consider the three topics for which experimental data are available: the quasifree-electron mobility, the resonant attachment of such electrons to molecular oxygen impurities, and electron self-trapping in the dense gas.

The complex angular momentum (CAM) approximation for nonrelativistic quantum scattering by a hard sphere–a union of the recently developed CAM uniform approximation with a semiclassical WKB-like approximation valid at large angles–is shown to be remarkably accurate over the complete range of scattering angles, and down to size parameters (circumference to de Broglie wavelength ratios) of order unity. The best approximations previously derivable (Fock-type) cannot reach large scattering angles where semiclassical approximations are useful; even at angles where Fock-type approximations are valid, they are typically two or more orders of magnitude less accurate than CAM. The crucial new feature responsible for the high accuracy of the CAM approximation is the treatment of large-angle diffraction associated with (a) tunneling near the edge of the scatterer, and (b) anomalous reflection.

After a general review of the analysis already available for back-action evasion schemes a perturbative approach is introduced and applied to a simple case. As a generalization of the back-action evasion schemes the concept of optimal pumping spectrum is introduced: it works for a unified treatment of stroboscopic and continuous quantum nondemolition strategies. Generalized back-action evasion strategies are introduced and studied in simple applications: they open the possibility for developing high-sensitivity schemes for the measurements of small forces. In particular, estimates of the noise figure for generalized back-action evasion transducers are discussed in detail.

We consider the rate at which one atom in a photodetector is ionized by a beam of classical light. A detailed examination of the probability of transition is presented, using first-order time-dependent perturbation theory and the rotating-wave approximation. This method usually leads to the well-known rule called ‘‘golden’’ by Fermi. We have made a more accurate analysis based on numerical quadrature techniques. We discover a curious oscillation in the probability for photoionization for short times and a temporal shift in the curve as compared to the result given by the golden rule. The shift is approximated analytically and found to correspond with the numerical result to a high precision. We also show results for the probability of photoionization without using the rotating-wave approximation.

We consider systems described by compact, periodic variables, such as Josephson junctions and small normal metal rings. We examine how they can be coupled to a heat bath, via either momentum or position coupling, and how the two descriptions can be related by a unitary transformation. We show how it is critical to transform not only the Hamiltonian, but also the initial conditions. We then demonstrate that for certain types of initial conditions, paths of different winding number can interfere. Still other, ostensibly reasonable initial conditions, have no such interference. We conclude with a discussion of appropriate models to describe periodic systems.

A method of evaluating perturbational components of intermolecular interaction energies by using quantum Monte Carlo (QMC) techniques is presented. It is shown how the nth-order Rayleigh-Schrödinger (RS) perturbation term may be expressed in a very compact way in terms of suitably defined stochastic autocorrelation functions of the perturbing operator (the intermolecular interaction potential). The resulting formula is very general (not restricted to intermolecular interactions) and corresponds in fact to an alternative way of expressing RS perturbation theory in any order. As concerns the exchange contribution responsible for repulsion at small distances, an approximate expression for the first-order exchange interaction energy (by far the leading component) is given. Both advantages and drawbacks of the proposed QMC approach with respect to more conventional ab initio perturbational treatments are discussed. Some test calculations for the interaction of two helium atoms at small distances are presented. Results are systematically compared to those obtained with ab initio perturbation calculations using large Gaussian basis sets.

The recoil corrections of order (Zα${)}^6$${\mathit{m}}^2$/M to the hydrogenic Lamb shift are reviewed, and additional terms previously thought to be small are calculated numerically. It is found that significant contributions arise from single-transverse–single-Coulomb interactions in which the bulk of the contribution comes from negative-energy electron intermediate states. This term is found to contain a lnZα dependence, which accounts for its large effect. Other smaller terms are also computed and combined with all previous Lamb-shift contributions. The current status of the Lamb shift in hydrogen is reviewed.

The theory of how excited-state hyperfine structure can be determined using a magnetic field to decouple the nuclear and electronic angular momentum is presented. The initial excited state is assumed to have an anisotropic Zeeman sublevel population distribution, which can be conveniently created by a laser-induced multiphoton excitation of an unpolarized atom. The Zeeman sublevel populations are subsequently mixed by the hyperfine interaction. The degree of mixing is controlled by a magnetic field applied along the quantization axis. The relative Zeeman sublevel populations can be monitored by detecting the polarization of fluorescence emitted when the excited state radiatively decays. It is convenient to take the ratio of two time-integrated fluorescent signals measured for orthogonal linear polarizations, since this is independent of the excited-state number density. The plot of this ratio versus magnetic field is very well approximated by a Lorentzian curve whose half-width is proportional to the magnetic dipole hyperfine coupling constant. This method was used to determine the magnitude of the magnetic dipole constant of the cesium 8${\mathit{D}}_{3/2}$ state to be 3.92±0.10 MHz, which is in excellent agreement with previous results.

A rigorous version of N- and v-representable energy density-functional theory, formulated in the context of local-scaling transformations, is advanced. The importance of N-representability conditions for the formulation of a density-functional theory that complies with the variational principle is discussed, and particular emphasis is placed in distinguishing functional from one-particle density N and v representability. It is shown, by resorting to local-scaling transformations, how it is possible to actually construct an energy density functional that at all points of variation is strictly equivalent to the expectation value of the N-particle wave function from which the one-particle density is obtained, that is, an energy density functional with built-in N-representability conditions. Some relationships between the present theory and those based on the Hohenberg-Kohn theorems are discussed. In illustration, simple applications of the present theory to two-electron systems are given.

The local-scaling transformation version of density-functional theory is extended to the case of spin-dependent densities. It is shown that, from the spin-dependent variational principle, there ensue spin-coupled Euler-Lagrange equations for the densities. The connection between the locally scaled external potential and the spin-dependent density is discussed.

A K-matrix method employing ${\mathit{L}}^2$ basis sets has been utilized to investigate the ${}_{}{}^1{}_{}{}^{}$P° continuum of helium between the N=2 and N=3 thresholds (65.4 –73.0 eV). The results include the partial and total photoionization cross sections, the asymmetry parameters β, and the positions and the widths of the autoionizing states. Good agreement is found with the available experimental data for the N=2 cross section. In agreement with other recent theoretical calculations, at 68.88 eV the total cross section is predicted to be slightly greater than the recommended value that is generally employed to normalize the experimental data.

The hyperfine field at the nucleus of singly ionized radium has been investigated using the relativistic linked-cluster many-body-perturbation-theory procedure, including the effects of distributed charge and magnetization over the nucleus. The total hyperfine field of 1239 T, when combined with the experimentally observed hyperfine constant for ${}_{}{}^{213}{}_{}{}^{}\mathrm{Ra}_{}^{+}{}_{}{}^{}$, yields a nuclear moment of 0.607(12)${\mathrm{\mu }}_{\mathit{N}}$, in excellent agreement with the experimentally observed moment of 0.6133(18)${\mathrm{\mu }}_{\mathit{N}}$ from Zeeman measurements. Our investigation leads to exchange core-polarization and correlation contributions of 14% and 13%, respectively, of the direct contribution of the 7s valence electron, these ratios being smaller than the corresponding ratios for the isoelectronic atom francium, in keeping with the expected trends for other isoelectronic alkaline-earth-metal ions and alkali-metal atoms. Comparison is made with the results of other calculations of the nuclear moment of ${}_{}{}^{213}{}_{}{}^{}\mathrm{Ra}$. Possible reasons for the success of the semiempirical Goudsmit-Fermi-Segre formula in predicting the hyperfine field in this ion and related systems will be discussed.

Various scattering cross sections such as differential, integrated-elastic, momentum-transfer, and total cross sections, and the spin-polarization parameters for both the elastic and the total scatterings of electrons and positrons from cadmium atoms in the impact-energy range of 6.4–300 eV, have been calculated relativistically by solving the Dirac equation. For the pure elastic-scattering case, the projectile-target interaction is represented by a real model potential that includes the static potential (attractive), a parameter-free polarization potential (attractive) and an electron-exchange potential for the electrons scattering, and the static potential (repulsive) and a parameter-free polarization potential (attractive) different from that of electrons scattering for the positrons scattering from cadmium. For the total scattering, which includes both the elastic-scattering and the inelastic-scattering processes, the total interaction is represented by a complex potential by adding a model absorption potential as its imaginary part. It has been observed that the agreement of the calculated differential cross section (DCS) curves for the elastic scattering of electrons from cadmium is reasonable with the previously measured values of DCS while the agreement is good with the recently measured values of DCS.

The following energy-transfer reactions have been observed in a Sr vapor following pulsed excitation of the 5 ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ state: ${\mathrm{Sr}}^{\mathrm{*}}$(5 ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$)+${\mathrm{Sr}}^{\mathrm{*}}$(5 ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$)→Sr(5 ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$)+${\mathrm{Sr}}^{\mathrm{*}\mathrm{*}}$(${\mathit{n}}^{2\mathit{S}+1\mathrm{}}$L)-ΔE, ${\mathrm{Sr}}^{\mathrm{*}}$(4 ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$) +${\mathrm{Sr}}^{\mathrm{*}}$(4 ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$)→Sr(5 ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$)+${\mathrm{Sr}}^{\mathrm{*}\mathrm{*}}$(${\mathit{n}}^{2\mathit{S}+1\mathrm{}}$L)-ΔE. The 4 ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$ state was populated by a nonlinear stimulated process. By measuring the rate coefficients for these reactions for over 40 final states ${\mathit{n}}^{2\mathit{S}+1\mathrm{}}$L, we look for insight into how these reactions depend on energy defect, spin, and angular momentum. It is found that there is not a very strong dependence on the energy defect, and that singlet and triplet final states are produced in comparable amounts. The final states tend to be populated more effectively as their angular momentum increases. Total rate coefficients are of the order of gas-kinetic rates.

The total inelastic cross section for electron-ion scattering may be found in the independent-processes approximation by adding the resonant cross section to the nonresonant background cross section. We study the validity of this approximation for electron excitation of multiply charged ions. The resonant-excitation cross section is calculated independently using distorted waves for various Li-like and Na-like ions using (N+1)-electron atomic-structure methods previously developed for the calculation of dielectronic-recombination cross sections. To check the effects of interference between the two scattering processes, we also carry out detailed close-coupling calculations for the same atomic ions using the R-matrix method. For low ionization stages, interference effects manifest themselves sometimes as strong window features in the close-coupling cross section, which are not present in the independent-processes cross section. For higher ionization stages, however, the resonance features found in the independent-processes approximation are found to be in good agreement with the close-coupling results.

Starting with the lowest-order unscreened QED matrix element for electron-positron pair production by heavy charged particles, we calculate the cross section for this process differential in all independent variables and valid for all pair energies small compared to the incident particle energy. Plane-wave solutions to the Dirac equation are used to represent the electron and positron in this calculation. The gauge-invariance condition is used throughout the calculation to separate the cross section into quantities that reduce to the Weizsäcker-Williams result in the appropriate limit and other terms that are not included in the Weizsäcker-Williams approximation. The accuracy of the Weizsäcker-Williams method, on which previous calculations of higher-order corrections were based, can thereby be estimated. Integration over the possible emission angles of one of the pair members gives an expression valid for low-energy pairs that can be compared with previous work based on the Weizsäcker-Williams method. Integration over the possible angles of the other pair member then gives an expression that turns out to be identical to one derived by Racah, as we show in detail, although some of the expressions given here prior to the second angular integration have not been given previously. The high energy-transfer limit of the expression for the cross section integrated over electron and positron angles is shown to be identical to that of Kelner in the unscreened case. Additional numerical integrations over the remaining variables are performed for a range of projectile energies using Kelner’s treatment of screening. These examples allow the determination of the accuracy of the Weizsäcker-Williams method as previously applied as a function of projectile and pair energy. The results for the total cross section, which include the correct behavior for low energy transfers, are compared with previous calculations.