For the first time to the authors’ knowledge a mathematically rigorous method is used for treating finite-time deviations from the exponential decay in the case of spontaneous Lyman-α transitions in a two-level hydrogenic atom. First, in the so-called Weisskopf-Wigner model (where the rotating-wave approximation is implied) finite-time deviations with a rigorous validity range, based on accurate error estimations, are derived. Second, in order to obtain the frequency shift (Lamb shift), counter-rotating terms are taken into account by using a projection-operator method developed a decade ago by one of the present authors [J. Seke, Phys. Rev. A 21, 2156 (1980)]. By means of this method, equations of motion for dipole-moment expectation values are derived without employing the usual Born approximation. These equations are solved by using the method of the Laplace transform and its inverse. Again finite-time deviations from the exponential decay of the dipole-moment expectation values with a definite validity range are obtained. Finally, it should be emphasized that all the results presented in this paper contain accurate error estimates which are absolutely necessary in a rigorous mathematical method.

Recently demonstrated techniques for measuring collision-induced phase in macroscopic optical coherence are described and analyzed in detail. The time-dependent phase measured by this method is used to study imaginary collision kernels for optical radiators that are related to the phase by Fourier transformation. The results indicate that classical velocity changes may make an important contribution to the imaginary kernel, in contrast to the real kernel, which is dominated by diffractive velocity changes.

The problem of time-dependent convection flow in a layer heated from below with no-slip boundaries is investigated in the case of electrically conducting fluids permeated by a homogeneous horizontal magnetic field. The Prandtl numbers of 0.1 and 0.025 are considered. Because the onset of oscillations is delayed owing to the presence of the magnetic field and because of the reduced heat transport in the case of traveling-wave convection, the Nusselt number is typically larger in the magnetic case. Convection in the form of symmetric traveling waves becomes unstable with respect to two different types of asymmetric disturbances. The monotonic asymmetric instability is preferred at high magnetic field strength, while the oscillatory asymmetric instability is found in the low-field case. The magnetic field can thus be used as a control parameter to follow the transition from one type of asymmetric wave convection to another.

An extensive set of measurements of the conductivity and dielectric constant of a three-component microemulsion system sodium di(2-ethylhexyl)sulfosuccinate–water–decane in the vicinity of a percolation threshold as a function of frequency (${10}^3$–${10}^9$ Hz) and volume fraction of the dispersed phase (20–64 %) has been made. The experimental data can be put into a form of a complex-conductivity scaling function containing indices that are related to static and dynamic percolation. The frequency dependence of the dielectric constant for all volume fractions studied can be well fitted by the Cole-Cole dispersion law which is closely related to the stretched exponential function in time domain known to describe relaxations in dense disordered systems.

A numerical technique, starting from the Boltzmann equation, for obtaining the time-dependent behavior of the electron-velocity distribution function in a gas is presented. A unique feature of this technique is that, unlike previously used procedures, it does not make use of any expansion of the distribution function. This allows the full anisotropy of the distribution function to be included in the solution. Furthermore, the problem associated with multiterm-expansion techniques of choosing a sufficient number of terms for convergence is completely avoided. The distribution function obtained by the present method is exact and, in principle, contains all of the expansion terms of the previous procedures. Details of the algorithm, including stability conditions, treatment of the boundaries, and evaluation of the collision integrals, are presented. This technique has been applied for obtaining the time-dependent behavior of electron swarms in gaseous argon and neon for various values of E/N (the ratio of the applied uniform dc field to the gas density), and the corresponding results are presented.

Velocity distribution functions showing kinematic compression and expansion are derived in the context of gravitational forces. Whereas kinematic compression is well known in laser ion-beam spectroscopy, kinematic expansion is a new concept. In our analysis, collisionless and weak-collision cases are considered. A brief discussion shows that the weak-collision case may be appropriate in certain regions of the interstellar medium and that kinematic compression and expansion could have interesting observational consequences. In particular, as we show elsewhere, kinematic expansion may be important in the formation of broad and asymmetric quasistellar object emission lines.

In order to evaluate the simultaneous influence of a neighboring ion located at an arbitrary distance R and of free electrons on atomic bound states in high-density plasmas ($N_e$≳${10}^{23}$ ${\mathrm{cm}}^{\mathrm{-}3}$) we have suggested a transient molecule model that consists of a two-ion center surrounded by bound and free electrons. The Dirichlet boundary condition is laid down in such a way to make the total electrostatic potential constant over the entire molecular envelope and also to obtain the limit of two independent ion spheres or that of one united ion sphere when R→∞ or R→0, respectively. A closed form has been obtained for the interaction potential between bound and free electrons at the high-temperature limit. Energy levels and wave functions have been evaluated by diagonalizing the total Hamiltonian in the subspace of the lowest 40 molecular levels. A possible appearance of new spectral components and, in particular, a drastic reduction of the Stark effect are clearly shown.

Using a simple analytical model, we examined the process of ultrahigh-pressure generation using ion-beam-driven flyers to impact on a stationary sample. The results suggested that pressures in excess of 5 Mbars can be attained in materials of medium densities even for a beam power density of ${10}^{11}$ W/${\mathrm{cm}}^2$ that is readily available with existing machines. This, together with the mm-size diameter of the ion beam on target and the lack of a high-temperature plasma corona, renders light-ion beams potentially a most powerful tool for laboratory high-pressure research.

Two-dimensional convection in a compressible hard-disk fluid confined between free boundaries is studied from both a microscopic and a macroscopic level, i.e., by molecular-dynamics (MD) simulation on the one hand and by (analytical and numerical) solution of the hydrodynamic equations on the other hand. For a fluid of 5000 hard disks in a rectangular box of an aspect ratio of 2, both approaches are in remarkable quantitative agreement, showing a stable double-roll convection pattern in the final state. From the hydrodynamical point of view the system is just beyond instability (R=1.07$R_c$) and involves the nonlinear coupling of two modes (codimension-2 bifurcation). The simplest and optimal system to study with MD has an aspect ratio of 1 and involves 1500 particles only. Here, a stable single-roll pattern is observed. The hydrodynamic analysis, though, displays less good quantitative agreement with MD, which is due to the stronger influence of microscopic boundary effects.

A source of the apparent deviation from three-dimensional (3D) Ising model behavior of the static critical phenomenon experimentally observed in several binary mixtures of water–nonionic-amphiphile systems has been identified. Analyses were made, in particular, on two ethylene glycol mono-n-dodecyl ether-water systems ${\mathrm{C}}_{12}$${\mathrm{E}}_5$-${\mathrm{H}}_2$O and ${\mathrm{C}}_{12}$${\mathrm{E}}_8$-${\mathrm{H}}_2$O (where E represents ether), for which a very extensive set of data has been published. Our analyses show that, in fact, all published experimental data are consistent with the 3D Ising exponents if several isochores, including the most critical one, are simultaneously analyzed using the linear model equations of state. Owing to the flatness of the coexistence curves it is experimentally rather hard to locate very precisely the critical concentration. With added difficulties of obtaining very pure amphiphile samples and correcting data for multiple-scattering contribution near the critical point in a conventional light-scattering experiment, the determination of the critical indices is always subject to large errors. All the sources of errors tend to lower the measured indices. For the dynamic critical phenomena, a combined use of the linear model equations of state and the full mode-coupling theory, including the background effect, allows us to fit all the dynamic light-scattering data along the ‘‘critical’’ and off-critical isochores by assuming a single value of the Debye cutoff wave number $q_D$ which is equal to the inverse of the average hydrodynamic diameter 2$R_H$ of the micelles. We point out the strong influence of the background effect on the critical concentration fluctuation dynamics for systems formed from unusually large objects in solution.

Cellular patterns of magnetic domains observed in uniaxial garnet films are comprised of three elemental domain structures: stripe segments, threefold vertices that join these segments, and pentagonal structures that join five segments and contain trapped magnetic bubbles. We report observations of the stability and dynamics of these structures and show how they govern the evolution of cellular patterns in an external bias field $H_B$. Energy localized in the stripe segments acts as tension that drives the domain motion. A simple extension of the conventional model of stripe domains incorporates domain interactions in sparse patterns and gives access to the bias and configuration dependence of the stripe tension. We apply this formulation to an array of stripe domains to characterize the tension that arises in nonequilibrium patterns. Comparison with experiment indicates that sparse, disordered (mazelike) stripe patterns maintain equilibrium as $H_B$ is monotonically increased and shows the expected divergence in stripe spacing at $H_B$=$H_{\mathrm{RI}}$, where $H_{\mathrm{RI}}$ is the run-in field for isolated stripe domains. In contrast, cellular patterns persist to $H_B$>$H_{\mathrm{RI}}$, where the patterns are far from equilibrium.

Vertex propagation is observed when the tensions in the adjoining stripe segments are unbalanced and leads to a reduction in total stripe length and cell density. The vertices are destroyed at a critical bias field $H_V$ (=0.79×4πM=151 Oe for our garnet sample) when the stripes are severed near the vertices. $H_V$ is the saturation field for cellular patterns and is significantly larger than that of any other observed domain configuration. Pentagonal bubble traps are also mobile and are destroyed by the collapse of the trapped bubble. A divergence of the average cell area which is limited by coercive friction occurs at the collapse field $H_5$ (=0.54 ×4πM=103 Oe) of an isolated bubble trap. Nonequilibrium cellular states arise in the regime $H_{\mathrm{RI}<H_B<H_5}$ when bubble traps resist collapse and obstruct the topological evolution. Coercive drag on the domain motion also results in nonequilibrium configurations and in some cases alters the pattern topology. We employ an ac field component to mitigate the effects of coercivity, and find that an amplitude several times larger than the coercive field $H_c$ is required to produce smooth dynamics and ensure reproducible, metastable, stationary states.

Quasiparticle transport in a degenerate molecular dimer obeying the nonlinear Schrödinger equation is studied in a dimer-state representation. Dissipation is introduced into a corresponding nonlinear Liouville–von Neumann equation as a stochastic parameter causing dephasing of the dimer-state evolution. A kinetic equation characterizing the difference of probability density on monomeric units of the dimer has been derived in the form of a nonlinear, second-order differential equation. Analysis of the equation and numerical solutions of the dynamics show that, depending on the interplay of the parameters, a quasiparticle can be self-trapped on the initial monomeric unit, be transferred to the second one, or probability density can be equalized over both monomers (sites).

We present experiments on the directional solidification of a moving nematic-isotropic interface. We study the bifurcation and marginal stability of the interface in a system of 4,4’-n-octylcyanobiphenyl (8CB) with the impurity hexachloroethane ${\mathrm{C}}_2$${\mathrm{Cl}}_6$ added. In the velocity, temperature-gradient parameter space, we can trace the marginal stability line, in qualitative agreement with theory. A quantitative analysis shows that three-dimensional effects, such as solute-driven convection and the thickness of the sample, must be considered.

A new Wigner phase-space distribution function is introduced for thermal quasiparticles currently in use in thermo field dynamics. The properties of this phase-space distribution are studied and compared with those of the corresponding zero-temperature distribution. Generalized uncertainty relations are implemented in order to study the explicit spreading in phase space as a function of temperature and quantum number of the thermal excitation, thereby permitting the investigation of quantum and thermal fluctuations.

Scaling properties of two-dimensional ballistic deposits grown at near-grazing angles of incidence are investigated analytically and numerically. We map the problem onto a system of coalescing Brownian particles and derive exact values for the static and dynamic surface exponents, ζ=1 and z=2, and for the exponents characterizing the self-affine columnar microstructure, τ=(4/3, ν=(2/3, and ${\nu }_{\perp }$=(1/3. This implies that the average column width increases as the square root of the deposit thickness. The distribution of surface step heights and the angular variation of the deposit density are also obtained analytically. The predictions are confirmed by large-scale computer simulations. Qualitative arguments are given to explain the slow crossover behavior at intermediate angles of incidence, which leads to apparently continuously varying scaling exponents. The substructure exponents for deposits grown at normal incidence are derived from a general scaling relation. We find τ=(7/5, νd∥=(3/5, and ν⊥=(2/5, in agreement with previous numerical work.

Adsorption transitions of polymers and crumpled membranes are studied for general substrate potentials in d-dimensional systems. Several regimes for the critical behavior are identified: (i) a weak-fluctuation regime for sufficiently long-ranged potentials which is well described by an ensemble of independent blobs; (ii) a complex intermediate fluctuation regime with infinite-order, second-order, and anomalous first-order transitions; and (iii) a strong-fluctuation regime for sufficiently short-ranged interactions which is characterized by second-order transitions with universal critical behavior.

The mean first-passage time (MFPT) of random walks on one-dimensional disordered lattice segments is considered. Disorder is modeled by prescribing random transition and sojourn probabilities to the lattice sites. We consider several models of disorder: models with symmetric and asymmetric random transition probabilities, random sojourn probabilities, and models with bond randomness. For these models we present exact results on the MFPT and disorder-averaged MFPT. We do not find any anomalous dependence of the disorder-averaged MFPT on the size of the lattice segment. The distribution of the MFPT resulting from the disorder is Gaussian for the models with symmetric and site symmetric transition probabilities and non-Gaussian for models with asymmetric transition probabilities.

The kinetics of nucleation and growth of thin films is investigated using phenomenological rate equations modified from the equations by Venables (Ref. 6). These consist of coupled first-order differential equations for single adatom density, stable-cluster density, and the fractional coverage of a layer. The rate of evolution of single adatom density on a substrate is governed by the flux of adatoms, the rates of desorption and adsorption of a single adatom, and incorporation of adatoms with other adatoms or with a stable cluster. This approach serves as a basis for a rate-equation model to describe multilayer growth. The effect of impurities is also discussed.

Multilayer growth using phenomenological rate equations is studied. These equations are developed from those for one-monolayer growth. The basic phenomena include the flux of atoms, desorption, and adsorption of a single adatom and incorporation of adatoms with other adatoms or with a stable cluster. In addition, we investigate the effect of migration of adatoms between layers. The same measures for growth modes are used as in our earlier Monte Carlo studies. These two approaches give consistent results. We conclude that the static and kinetic approaches to determine growth modes differ substantially.

The relaxation properties of a one-dimensional overdamped system modulated by an external periodic force are studied analytically by means of a perturbation approach. The validity of the approximations introduced is discussed in detail. The nonstationary nature of the process is illustrated by evaluating explicitly the autocorrelation function for the relaxation in a bistable potential. The predictions thus obtained are shown to compare favorably with the results of analogue simulation for the case of a quartic double-well potential. The stochastic resonance mechanism is proven to set in only when the periodic perturbation breaks the symmetry of the bistable potential.