We study the phase-space behavior of the standard two-level system (spin 1/2) coupled to a harmonic oscillator (without the rotating-wave approximation), the classical counterpart of which is known to display deterministic chaos. We study the quantum-mechanical phase-space behavior by means of harmonic-oscillator coherent states (Husimi representation). Stationary quantum Poincaré sections may be defined; they show many parallels to their classical counterparts. We also study the time development of initially coherent states and observe a tendency towards a decay into many small wave packets in phase space for parameters in the chaotic regime.

The pion charge-exchange probability in hydrogen for stopped ${\mathrm{\pi }}^{\mathrm{-}}$ has been measured for a series of alcohols. The relative atomic capture probabilities for hydrogen in different chemical environments as well as for the other molecular constituents were extracted from the data using a phenomenological approach. The results allow the prediction of the charge-exchange probability in other molecules of similar chemical structure. The charge-exchange probability in deuterated methanols was measured and compared to the prediction of our model. A comprehensive picture is obtained if pion transfer from hydrogen to deuterium is included.

Thermodynamic and multifractal spectra of chaotic scattering are investigated at abrupt bifurcations leading from fully developed chaotic to regular scattering as the particle energy $E$ passes through a critical value $E_m$. For processes with uniform scaling, the spectra of Lyapunov exponents, entropies, and partial dimensions diverge, stay constant, and vanish, respectively, when the energy approaches $E_m$ from below. To characterize processes also having scattering angles close to 90°, a new quantity is introduced, the partial topological entropy depending on the concentration of single scatterings with angles close to 90°. Multifractal spectra are proved to be universal in the sense that they depend on topological properties only. In particular, the generalized dimensions scale as $D_q=\frac{d_q}{\left|\ln \right(E_m-E\left)\right|}$ for $q$ of order $\frac{1}{\left|\ln \right(E_m-E\left)\right|}$, otherwise, $D_q$ is finite and zero in the negative and positive $q$ ranges, respectively. Our approach thus justifies a conjecture of Bleher, Ott, and Grebogi [Phys. Rev. Lett. 63, 919 (1989)] for $q=0\mathrm{}$, and yields explicit expressions for the coefficients $d_q$. Phase transitions arising at the bifurcation point are analyzed.

The decay statistics of ${}_{}{}^{90}{}_{}{}^{}\mathrm{Y}$ have been studied from the count data collected during the radioactive ${\mathrm{\beta }}^{\mathrm{-}}$ decay from a carrier-free isotope of ${}_{}{}^{90}{}_{}{}^{}\mathrm{-}_{}^{90}{}_{}{}^{}$Y. The values of the relative Allan variance exceeded those predicted for a simple Poissonian process for counting times longer than 10 min and reached a limiting value called the flicker floor attributed to 1/f fluctuations. This study was extended for various energies of the ${}_{}{}^{90}{}_{}{}^{}\mathrm{Y}$ spectrum.

The motion of a periodically forced, damped anharmonic oscillator governed by the equation of motion, x¨+vẋ=${\mathit{A}}_2$x+${\mathit{A}}_4$${\mathit{x}}^3$+${\mathit{A}}_6$${\mathit{x}}^5$+F cos(Ωt), has been studied. The analysis of the response function of this equation when treated analytically, and later, numerically, uncovers a hysteresis-type phenomenon. The stability and response of the system and the onset of period doubling have been observed through an analytical approach, and they are corroborated with a numerical analysis for different values of F and Ω (Ω is the frequency of the periodic forcing system). Two different methods have been used. In the first, the damped system is converted into an undamped one by making an ansatz for ẋ of the form ẋ=R(x), a polynomial in x. The second approach, however, studies the system directly. It has been observed that there exists a wide difference between these two systems. Furthermore, period doubling may be predicted through the use of the harmonic balance technique and Mathieu equation. Lastly, a numerical integration in phase space clearly indicates orbits corresponding to the initial period, then to double the initial period, and subsequently to higher multiples.

We illustrate the perturbative nature of Wigner-Kirkwood expansions showing that for strongly repulsive potentials quantum corrections are not properly taken into account. We then present an alternative calculation of quantum corrections for such cases based on well-known semiclassical methods. We begin with a simple example and then go on to consider a semiclassical expansion for the propagator of a particle in the vicinity of the boundary of a sphere and show that by treating the classical physics nonperturbatively an extra term, corresponding to reflection, appears in addition to the Wigner-Kirkwood term. We calculate quantum corrections to all orders and sum the semiclassical series, recovering the results of previous authors for both the propagator and the direct second virial coefficient. We conclude with a discussion of the implications of our analysis for more general potentials.

We have shown that finite-size effects in the correlation functions away from equilibrium may be introduced through dimensionless numbers: the Nusselt numbers, accounting for both the nature of the boundaries and the size of the system. From an analysis based on fluctuating hydrodynamics, we conclude that the mean-square fluctuations satisfy scaling laws, since they depend only on the dimensionless numbers in addition to reduced variables. We focus on the case of diffusion modes and describe some physical situations in which finite-size effects may be relevant.

We have carried out a number of simulations to study the dynamical behavior of kinks in the ${\mathrm{\phi }}^4$ model in the presence of strong fluctuations of its double-well potential. Our work widens the computational and analytical knowledge of this system in four directions. First, we describe in detail a numerical procedure that can be easily generalized to other stochastic, soliton-bearing equations. We demonstrate that it exhibits consistency features never found in previous research on nonlinear stochastic partial differential equations. Second, we fix the range of validity of theoretical approaches based on secular perturbative expansions. We show how this range depends on a combination of noise strength and duration. Third, we numerically study the model beyond the applicability of analytical methods. We compute the main characteristics of kink dynamics in this regime and discuss their stability under this random perturbation. Finally, we introduce dissipation and boundaries in the dynamically disordered model. We establish that the essential consequence of friction action is to soften the noise effects, while boundaries give rise to a critical velocity below which kinks cannot enter the noisy zone.

Transport of muonic deuterium atoms in a slab of thickness d filled with a molecular deuterium gas is described by means of the multiple-collision expansion in the framework of a time-dependent theory. The relevant expressions for the emerging flux are derived. Numerically generated results are presented for several different cases, some of which are under experimental investigation. A justification of the approximations made in a previous work is given.

Screening constants σ are given for one-electron basis-set radial wave functions for atomic systems with 2≤Z≤18. The parameters σ for an individual screened electron (i) are dependent on the states of the screening electron (j), and the matrix of values ${\mathrm{\sigma }}_{\mathit{i}\mathit{j}}$ is different from that suggested long ago by Slater [Phys. Rev. 36, 57 (1930)]. The matrix is slightly more complicated than Slater’s, but the results for individual electron binding energies are much more accurate—even comparable in accuracy with Hartree-Fock (HF) values. The procedure is applied to compute both inner- and outer-shell binding energies, and a comparison is made with other similar calculations as well as with the HF and experimental values. The K-shell binding energies ${\mathit{E}}_{\mathit{K}}$ calculated with the new screening constants are in particularly close agreement with the results of HF calculations and with experimental values for elements for which accurate measurements can be made for gaseous atomic species. The quantities ${\mathit{E}}_{\mathit{K}}$ computed for C, N, and O atoms by the screening-constant method, while in agreement with HF calculations, differ from the values now being employed to evaluate the x-ray opacity of the interstellar gas. These currently used K threshold energies have not been measured for gaseous monatomic matter and are off by 2–6 %; the theoretical ${\mathit{E}}_{\mathit{K}}$ are very likely more accurate and should be adopted. A simple prescription is suggested for modifying the screening-constant wave functions for 2p states. Uncorrected, these functions, which are hydrogenic, fall off too fast at large r. Adding a single additional exponential term gives a much better fit to the HF functions, and a universal coefficient is suggested for this term. The prescription yields good agreement with HF values for 〈r〉 and 〈${\mathit{r}}^2$〉 for the species B to Ne; the computed diamagnetic susceptibility for Ne using the simple modified wave function agrees well with the experimental value.

We consider a nonlinear partial differential equation that arises in the study of Hopf bifurcation in extended systems, as in the Kapitza problem. The equation in one space variable and time has dispersion and dissipation, and it is invariant under translation and Galilean boost. This equation contains the Burgers, Korteweg–de Vries, and Kuramoto-Sivashinsky equations as special cases. Numerical studies reveal that the complicated solutions of this equation may be seen as a mixture of elementary, pulselike solutions that, in the course of time, lock in and form stable lattices for a wide range of system parameters. By describing such states as bound states of single pulses, we can calculate the lattice spacings accurately–a simple formula gives these spacings. We also use this multiparticle description to derive equations of motion of unbound, interacting pulses. These equations go to the proper asymptotic states and provide a qualitatively plausible description. However, some quantitative discrepancies with the numerical simulations suggest that further aspects of such problems deserve further exploration.

We solve numerically both the deterministic stochastic Swift-Hohenberg equation [J. Swift and P. C. Hohenberg, Phys. Rev. A 15, 319 (1977)] in one spatial dimension. In the deterministic case we address the question of pattern selection by studying the temporal evolution away from a uniform, unstable solution. The asymptotic stationary solutions found are periodic in space with a range of wave numbers that is narrow, and consistent with earlier theoretical predictions on the range of allowable periodicities in a finite system. In the stochastic case, the power spectrum of the stationary solutions is very broad and typical configurations do not have a well-defined periodicity. A correlation length is defined that measures the extent over which a stationary solution is periodic. We find that the correlation length is finite, smaller than the size of the system studied and decreases with the amplitude of the stochastic contribution. We confirm these findings by performing a Monte Carlo heat-bath simulation that directly samples the stationary probability distribution function associated with the Lyapunov functional from which the Swift-Hohenberg equation is derived.

A lattice model of a two-component fluid that displays a closed-loop phase diagram is studied to determine the correlated site percolation threshold of one of the components. Both the phase diagram and the threshold of the three-dimensional system are determined within the Bethe approximation. A rapid variation of the threshold with temperature below the lower critical point is found, similar to that observed in a recent experiment. This variation is attributed to the tendency of the interactions to structure the fluid.

We have used a molecular-dynamics simulation to calculate the first seven nonzero Legendre coefficients, ${\mathit{Q}}^{\left(\mathit{l}\right)}$(r,r’), of the static pair-pair correlation function Q(r,r’). The interaction potential was taken to be Lennard-Jones. The simulations were done at two different values of density and temperature, one coinciding with that of liquid argon near its triple point and the other with liquid argon at 181.0 K. Q(r,r’) can be expressed in terms of two, three-, and four-body distribution functions. We use the Kirkwood superposition approximation to estimate the three-body contribution to Q(r,r’). We argue that at low densities the three-body correlations are substantially more important than the four-body correlations. The three-body part of the l=4 and 6 coefficients emphasizes configurations composed of nearest-neighbor triplets with internal angles of approximately 90° and 60°, respectively. We find that the l=6 coefficient shows a dramatic increase in structure at elevated density. Furthermore, this coefficient exhibits nearly periodic oscillations in its off-diagonal structure. Directions for future work are given.

We extend previous work on the Khokhlov-Semenov approach to long-range order in solutions of persistent flexible main-chain polymers by including hexagonal columnar ordering. The description of long-range positional order uses a recent model developed for rigid rodlike particles, which is based on the tradeoff of translational entropy between liquidlike and crystal-like dimensions. For moderately flexible polymers, we find an isotropic-nematic-columnar phase sequence with increasing polymer concentration. As the polymers become more flexible, the isotropic-nematic transition recedes to higher concentrations, until finally, near the wormlike chain limit, a direct isotropic-to-columnar transition occurs. We show that the corresponding triple point occurs at longer persistence lengths for polymers of increasing contour length. In addition, we show that the longitudinal packing in the columnar phase becomes much tighter with increasing molecular flexibility to accommodate greater lateral freedom. Finally, we compare our theoretical equation of state with experimental measurements for poly-benzyl-L-glutamate (PBLG).

It has been shown in our previous paper [Phys. Rev. A 40, 6431 (1989)] that repulsive hydration forces between parallel hydrophilic surfaces separated by a thin water film are determined by the lateral distribution of solvated surface groups. This theory is now extended to include correlations in fluctuations of the solvated group distribution between the opposing surfaces. The solution is obtained in a treatment formally analogous to the ‘‘spherical model’’ for Ising systems. It is shown that the correlations between the opposing surfaces give an attractive contribution to the hydration forces. Conditions governing the crossover from net repulsion to net attraction are studied. Hydration attraction appears and increases gradually with a decrease in temperature below a critical value or with variation of other system parameters. Full transition to the net attractive force leads to formation of a dehydrated contact between the surfaces. The results are applied to describe dehydration transitions in multilayer lipid systems.

Structural slowing down in a simple model of a polydisperse suspension of charge-stabilized colloidal particles is explored by molecular-dynamics and Brownian-dynamics simulations. The former ignore solvent effects, but allow a comparison with recent experimental, numerical, and theoretical work on ‘‘fragile’’ glass formers. Solvent friction is taken care of in the irreversible Brownian-dynamics simulations, but solvent-induced hydrodynamic interactions between colloidal particles are neglected. Self-diffusion is found to proceed by hopping processes, near and below the kinetic glass transition temperature, even in the case of Brownian dynamics, where cooperative phonon processes are overdamped. Newtonian and Brownian dynamics lead to qualitatively different relaxations of the density fluctuations. The density autocorrelation functions calculated with Brownian equations of motion show no evidence of β relaxation. The simulation results are discussed in the light of recent dynamic-light-scattering experiments on concentrated colloidal suspensions.

Vesicle shapes of low energy are studied for two variants of a continuum model for the bending energy of the bilayer: (i) the spontaneous-curvature model and (ii) the bilayer-coupling model, in which an additional constraint for the area difference of the two monolayers is imposed. We systematically investigate four branches of axisymmetric shapes: (i) the prolate-dumbbell shapes; (ii) the pear-shaped vesicles, which are intimately related to budding; (iii) the oblate-discocyte shapes; and (iv) the stomatocytes. These branches end up at limit shapes where either the membrane self-intersects or two (or more) shapes are connected by an infinitesimally narrow neck. The latter limit shape requires a certain condition between the curvatures of the adjacent shape and the spontaneous curvature. For both models, the phase diagram is determined, which is given by the shape of lowest bending energy for a given volume-to-area ratio and a given spontaneous curvature or area difference, respectively. The transitions between different shapes are continuous for the bilayer-coupling model, while most of the transitions are discontinuous in the spontaneous-curvature model. We introduce trajectories into these phase diagrams that correspond to a change in temperature and osmotic conditions. For the bilayer-coupling model, we find extreme sensitivity to an asymmetry in the monolayer expansivity. Both models lead to different predictions for typical trajectories, such as budding trajectories or oblate-stomatocyte transitions. Our study thus should provide the basis for an experimental test of both variants of the curvature model.

We develop an analytical method to extend the two-parameter family of analytical solutions in channel geometry to sector geometry with arbitrary opening angle at zero surface tension. We then show how to apply the WKB method to select the limiting finger width at very small surface tension. The result agrees very well with experiment. We also discuss stability of the pattern based on the special structure of these selected solutions.

The relativistic linked-cluster many-body perturbation theory has been applied to calculate the hyperfine fields in the ${\mathrm{Zn}}^{+}$, ${\mathrm{Cd}}^{+}$, and ${\mathrm{Hg}}^{+}$ ions. We calculate field strengths of 451±9, 795±15, and 2642±63 T, respectively, values in good agreement with experiment for ${\mathrm{Cd}}^{+}$, and in excellent agreement for ${\mathrm{Hg}}^{+}$. No experimental data are available for the ${\mathrm{Zn}}^{+}$ system. We will discuss the contributions to these total fields coming from the valence, one-electron perturbation, and many-body correlation mechanisms, and compare these contributions with those calculated in the alkali-metal atom and alkaline-earth ion systems that also have a single electron outside closed shells. We will also discuss the importance of third- and higher-order correlation contributions, which are rather large in these systems.