The ground-state energy of the quadratic Zeeman Hamiltonian ${\mathit{p}}^2$/2-Z/‖x‖+${\lambda }^2$(${\mathit{x}}_1^2$+${\mathit{x}}_2^2$)/2 has been approached using 2+ε space dimensions in conjunction with the virial and Hellmann-Feynman theorems. Series expansions to first-ε order have been performed, thereby setting ε=1 in the end of the calculations. The ground-state energy established in this way exhibits good accuracy for strong and very strong fields, e.g., for 1<λ≤${10}^3$. However, if λ<1, one has certain intervals in which the accuracy of this method becomes poorer.

A nonlinear calculation of the dynamics of transient pattern formation in the Fréedericksz transition is presented. A Gaussian decoupling is used to calculate the time dependence of the structure factor. The calculation confirms the range of validity of linear calculations argued in earlier work. In addition, it describes the decay of the transient pattern.

We present a direct numerical test of the Yamada-Kawasaki representation of nonlinear isothermal response theory. We show that phase averages calculated using the explicitly normalized Yamada-Kawasaki distribution function agree with those calculated directly from computer simulation.

In their recent paper [Phys. Rev. A 35, 4122 (1987)] Castrigiano and Kokiantonis claim to present an exact calculation of the partition function for a quantum oscillator interacting with the blackbody radiation field. In this Comment it is shown that their result is in fact wrong, due essentially to their neglect at the outset of the $A^2$ term in the Hamiltonian. It is further shown how their error can be repaired to give the correct result given by us in an earlier publication [Phys. Rev. Lett. 55, 2273 (1985)].

We have studied ${\mathrm{H}}^{+}$+He and ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{++}{}_{}{}^{}$+He ionizing collisions at intermediate energies (60 to 120 keV/amu) and have observed a significant shift in the velocity position of the maxima in forward-ejected electron spectra when changing projectiles from protons to α particles. In ionizing collisions, a large portion of the ejected electrons are stranded near the transitory equiforce, or saddle point, position between the target ion and receding projectile. The shift in the electron spectra maxima to smaller velocities, due to changing projectiles from protons to α particles, is consistent with the shift in the saddle-point velocity when the projectile charge is increased.

We report the first high-resolution angle-resolved electron spectra of helium photoionized above threshold by intense, linear or circularly polarized 532-nm laser pulses. Quantitative comparisons are made to the Keldysh-Faisal-Reiss theory of photoionization in intense fields.

Ground-state phase transitions of the degenerate parametric amplifier assuming the pump mode in an ordinary coherent state and the signal mode in an SU(1,1) coherent state are discussed. A second-order phase transition with the coupling constant playing the role of a control parameter is found. The lower-energy state can be a squeezed state in the signal mode. An additional anharmonic term related to optical bistability is shown to enhance the effect.

Experimental study is presented of an electron temperature in an intense soft-x-ray heated plasma through extreme ultraviolet spectroscopy. Temperatures obtained from time integrated x-ray line and continuum emissions were found to be $T_e$=53$I_x$${(10\mathrm{}}^{13}$ W/${\mathrm{cm}}^2$${)}^{0.29}$(eV) for Al plasma over the range of intensities of ${10}^{12}$ to 6×${10}^{12}$ W/${\mathrm{cm}}^2$. The intensity scaling of temperature is compared with an analytical model and is found to agree well with this model.

Dynamic light scattering is observed for an entanglement gel, gellan gum, whose solvent is a critical mixture of isobutyric acid and water. We observe a length scale, $l_x$, below which the sample shows two correlation times and above which only one (diffusive) correlation time is seen. This length scale grows as a power law as T→$T_c$. Several observed features of this system, including critical exponents for dynamic and static light scattering, are inconsistent with available model estimates.

We derive an approximate Fokker-Planck equation up to first order in the correlation time for a stochastically forced Hopf bifurcation. The general results are illustrated on the Brusselator model. In the range of validity of our approximation, it is shown that the noise always postpones the bifurcation point (appearance of new extrema of the probability distribution). This shift is a decreasing function of the correlation time. Qualitative agreement is found with recent experimental observations [L. Fronzoni, R. Mannella, P. Mc Clintock, and F. Moss, Phys. Rev. A 36, 834 (1987)].

Rigorous lower bounds to a class of density-dependent quantities (specifically, those of the form F${\rho }^n$$d^D$r) of D-dimensional physical systems are found in terms of the moments around the origin (or radial expectation values 〈$r^{\alpha }$〉 with negative and positive α) of the single-particle density ρ(r) in a compact and simple form. They allow one to obtain lower bounds to kinetic energy and upper bounds to the exchange energy of many-fermion systems in arbitrary spatial dimensions within the plane-wave approximation (e.g., Thomas-Fermi model) and also in a model-independent way. The large-D limit is also studied. Several results encountered by various authors for real (D=3) fermion systems (e.g., atoms, nuclei) are obtained as particular cases.

We report the first observations of a strong damping and velocity anomaly in an ultrasonic wave in the vicinity of the smectic-A–hexatic-B phase transition. These effects are markedly anisotropic, and reflect the hexatic order-parameter fluctuations.

We present numerical simulations of long Josephson junctions in the presence of an rf bias and an applied magnetic field, which we model with a sine-Gordon-like equation. We focus our attention on quasiperiodic and chaotic dynamics and their transitions. We show that quasiperiodicity arises from the competition between two incommensurate frequencies: one due to the success of the system in exciting a solitonlike structure and the second one due to the rf drive. We demonstrate the universality of the multifractal structure of the attractor at the onset of chaos.

The relationship between structural properties of growing patterns and their cluster statistics is discussed. We consider the cases in which an entire pattern grown from a $d_s$-dimensional substrate is self-similar with a fractal dimension D, whereas individual clusters constituting it are self-affine with exponents ${\nu }_{?}$ and ${\nu }_{\perp }$ for the scaling behavior of the height and width, respectively. Based on a scaling assumption for the cluster-size distribution function ($n_s$∼$s^{\mathrm{-}\tau }$; s is the cluster size), the scaling relation τ=2-${\nu }_{?}$(D-$d_s$) is derived. It is found that the relation is in excellent agreement with almost all available simulation data for growth models investigated so far.

The occurrence of resonant states in regions of high potential, inferred from experiments over two decades, is traced to a familiar aspect of the diagonalization of finite Hamiltonian matrices. The diagonalization generates two sets of eigenstates localized in regions of high and low potential, respectively. These sets are related by a conjugation transformation that determines the relative numbers of set elements and the scale ratio of their eigenvalue spectra. The residual eigenstates are not localized.

It is demonstrated for the three-dimensional three-particle system that a divergence arising from essentially the same singularity structure of the kernel of the scattering integral equation is responsible for both the Efimov and Thomas effects. The above divergence implies that the results of a three-particle dynamical calculation will be sensitive to the details of the two-particle interaction. In two-dimensional systems, the above divergence is absent and consequently the three-particle observables become essentially independent of the two-particle interaction model.

We derive the quantum-mechanical tunneling transmission coefficient for energies near the peak of a general potential barrier, to fourth order in the Wentzel-Kramers-Brillouin (WKB) approximation, using a method based on an eighth-order Taylor expansion of the potential near the peak. The result agrees with contour-integral formulations of WKB tunneling. For the Pöschl-Teller potential the WKB series converges rapidly to the known exact transmission coefficient. Higher-order WKB corrections may be important in attempts to determine the internuclear potential by inversion using low-energy fusion cross-section data.

Electron-attachment cross sections are reported in the electron energy range 0–150 meV, at an energy resolution of 6.5 meV (full width at half maximum) for the molecules HI and DI. Use is made of the Kr photoionization method to obtain cross sections for HI, and a signal intercomparison technique to obtain cross sections and the thermal-attachment rate constant for DI. Attachment properties of the two molecules are very similar. The ratio of attachment cross sections is discussed in terms of the reduced-mass dependence of the dissociation width and the survival probability, and in terms of spectroscopic thresholds and rotational populations for attachment at 300 K. Approximate potential-energy curves for the lowest states of the neutral molecule and negative ion are given.