A numerical method of integration of the time-dependent Schrödinger equation is presented for the hydrogen atom and for the ${\mathrm{H}}_2^{+}$ molecule. Cylindrical coordinates are used and the wave function is expressed as a Bessel-Fourier series. This expansion allows one to eliminate singularities present in the Hamiltonian and to use a unitary split operator to evaluate numerically multiphoton transitions. Laser-induced ionization rates for ${\mathrm{H}}_2^{+}$ are calculated and compared with rates for the hydrogen atom. A strong dependence of the ${\mathrm{H}}_2^{+}$ ionization rates on the initial vibrational excitation is found.

We analyze the relationship between the phase distribution for optical fields derived using phase-operator techniques with that derived from the Wigner phase-space quantum quasiprobability. We show that these two approaches agree for field states dominated by Fock states within a narrow distribution, but differ for cases involving widely separated photon-number contributions. Dominance by even Fock states can result in a negative Wigner phase distribution. An example of this is drawn from the Jaynes-Cummings model.

We propose a method to investigate the phase dynamics of the radiation field of a micromaser in steady-state operation. The phase-diffusion information is deduced from the population statistics of the atoms leaving a classical coherent field placed after the micromaser cavity. By using the classical coherent field, one gains an additional degree of freedom which allows one to probe the polarization component of the atomic dipole which is directly correlated to the cavity-field amplitude. As an illustration we present the results of a computer experiment, modeling the complete dynamics of the proposed experiment.

We study analytically and numerically the reaction kinetics for diffusion-limited reactions of the type A+B(static)→C(inert) in one-dimensional systems with reactants initially separated in space. We find expressions for the concentration profiles for each species, and for the reaction front. The width of the front is characterized by w∼${\mathit{t}}^{\mathrm{\alpha }}$ with α=1/4, and its height by h∼${\mathit{t}}^{\mathrm{-}\mathrm{\beta }}$ with β=3/4; these values differ from the ‘‘mean-field’’ exponents and those obtained when both species diffuse.

A simple model that describes traffic flow in two dimensions is studied. A sharp jamming transition is found that separates between the low-density dynamical phase in which all cars move at maximal speed and the high-density jammed phase in which they are all stopped. Self-organization effects in both phases are studied and discussed.

We simulate ballistic deposition with long-range temporal correlated noise of bounded amplitude in 1+1 dimensions. Good agreement with the dynamical renormalization-group calculation of Medina et al. [Phys. Rev. A 39, 3053 (1989)] is obtained for the scaling exponents when the noise is generated by a version of Mandelbrot’s fast fractional Gaussian noise (FFGN) generator. However, using the original FFGN, other exponents are obtained. We suggest that this error is due to an extraordinarily slow crossover caused by the existence of an anomalous growth mode incompatible with the KPZ equation. This may have implications on similar model-dependent results for recent simulations on growth with power-law noise and spatially correlated noise.

The effect of energy conservation on the decomposition dynamics of unstable states is considered for systems with nonconserved order parameters. We demonstrate that close to the critical point of instability the dynamics of the order parameter field is described by the nonlinear Cahn-Hilliard equation, leading to microstructure evolution by heat-transfer-controlled modulation. The results are applied to first-order displacive transitions, predicting an alternative transformation mechanism that follows a path of continuous strain modulation with finite wavelength.

A theoretical sandpile model with stochastic slide is proposed. A damping length scale is found in this model. The systems belong to different classes of universality depending on the relationship of their linear size to the damping length scale. A numerical study shows that the behavior of this model is close to a recent experiment of sandpile by Held and co-workers [Phys. Rev. Lett. 65, 1120 (1990)].

A system of particles hopping on a line, singly or as merged pairs, and annihilating in groups of three on encounters, is solved exactly for certain symmetrical initial conditions. The functional form of the density is nearly identical to that found in two-body annihilation, and both systems show ∼1/ √t decrease of particle density for large times.

We describe a new traveling-wave cross-roll state in a water-filled cylindrical convection cell with thermally conducting sidewalls (Γ=D/2d=4.94). Just beyond convective onset, four axisymmetric toroidal rolls form. For ε=(R-${\mathit{R}}_{\mathit{c}}$)/${\mathit{R}}_{\mathit{c}}$>0.15 this pattern loses stability to either a nonaxisymmetric state with rolls normal to the sidewall, or (by skipping from onset to a value of 0.3<ε<1.3) a pattern consisting of three toroidal rolls with cross rolls in the outermost toroidal roll. The cross rolls are time dependent and typically form modulated traveling waves.

The results of an asymptotic analysis of the probability distribution for the three-dimensional vector of velocity increments in turbulent flow are presented for the case of large fluctuations. This asymptotic regime is determined by the inertial relative motion of fluid particles, subject to the constraint of incompressibility. The obtained joint probability density for radial and transverse components of velocity increments has a peculiar form.

The detailed behavior at the onset of Rayleigh-Bénard convection is examined using molecular-dynamics simulation of a hard-disk fluid in which the vertical temperature difference is increased gradually. The dependence of thermal flux and mass transfer rate on Rayleigh number just above onset is shown to be consistent with the assumption that the convective bifurcation is the analog of a second-order phase transition.

We study phase ordering in nematic liquid crystals using cell-dynamics simulations for d=2, n=2, and d=3, n=3. The tail in the structure function decays as ${\mathit{k}}^{\mathrm{-}\mathrm{\chi }}$, with χ=4.0±0.1 for d=2 and χ=5.3±0.1 for d=3. We compare these values to results of Bray and Puri [Phys. Rev. Lett. 99, 99 (1992)] for a vector order parameter and to experimental measurements. For the d=3 system the characteristic length scale in the system varies as L(t)∼${\mathit{t}}^{\mathrm{\phi }}$, with φ=0.44±0.01.

The spreading of smectic-A droplets on a smooth, high-energy surface has been studied using x-ray reflectivity, ellipsometry, and video imaging at the Brewster angle. These droplets have a layered structure and terraces are evidenced. The dynamics of expansion or retraction of these terraces are investigated and compared with recent theoretical predictions. In a last stage, holes open in the single remaining terrace and their growth ultimately leads to a complete breaking up of the terrace. The nematic and isotropic phases dewet the first terrace, and holes also appear in the layer by raising the temperature above the smectic domain.

Detailed heat-capacity measurements have been carried out on free-standing liquid-crystal films of n-heptyl-4’-n-pentyloxybisphenyl-4-carboxylate to investigate the nature of transitions related to surface crystal-E order. Distinct thermal hystereses are observed. Upon heating from the temperature range exhibiting surface crystal-E order and interior hexatic order, anomalous effects on the interior hexatic-B–smectic-A transition, which strongly depend on the film thickness, are evident.

Observation of a continuous thermodynamic path between smectic-${\mathit{A}}_1$ and smectic-${\mathit{A}}_2$ phases is reported. This path follows a continuous evolution from smectic-${\mathit{A}}_1$ to smectic-${\mathit{A}}_{\mathit{d}}$ in the vicinity of a closed-loop nematic domain and then from smectic-${\mathit{A}}_{\mathit{d}}$ to smectic-${\mathit{A}}_2$ in the neighborhood of a smectic-${\mathit{A}}_{\mathit{d}}$–smectic-${\mathit{A}}_2$ critical point.

We determine the asymptotic behavior of the orientationally averaged structure factor S(q) for a large, flat membrane characterized by a roughness exponent ζ. We show that S(q)∼1/${\mathit{q}}^2$ for q≪1/l, where l is controlled by the amplitude for transverse or longitudinal fluctuations. If l is much larger than the intermonomer distance a and 1/l≪q≪1/a, then S(q)∼1/${\mathit{q}}^{3\mathrm{-}\mathrm{\zeta }}$ or S(q)∼1/${\mathit{q}}^{4/\mathrm{\zeta }\mathrm{-}2}$ for a small or large amplitude for longitudinal fluctuations, respectively. We also consider the case where the surface is self-affine only at large distances.

To explain the observed deviation from the Rapini-Papoular surface energy of nematic-liquid-crystals, we propose a model of the form Tr[(${\mathit{Q}}_{\mathit{i}\mathit{j}}$-${\mathit{Q}}_{0\mathit{i}\mathit{j}}$${)}^2$] (${\mathit{Q}}_{\mathit{i}\mathit{j}}$ is the quadrupolar order parameter of the nematic-liquid-crystal and ${\mathit{Q}}_{0\mathit{i}\mathit{j}}$ a quadrupolar surface field). For a broken anchoring, this model predicts a surface order decrease ΔS≊3/2(ξ/d)${\mathit{S}}_{\mathit{B}}$ where ξ and d are the coherence and surface extrapolation lengths of the nematic liquid crystal and ${\mathit{S}}_{\mathit{B}}$ is the bulk order parameter. A quantitative check is presented on planar anchoring of various strengths and temperatures.

A simple model is derived that describes the nonlinear interaction of an ultra-short laser pulse with a coherent Langmuir wave. It is shown that the laser frequency can be increased by an order of magnitude using highly relativistic plasma oscillations. The bifurcation value of the electromagnetic energy, i.e., the value when the pulse ceases to accelerate due to its own nonlinearity and starts to enhance the Langmuir wake field, is determined.

In the marginally stable ordered state of Kohonen’s feature-map neural-network model the distribution of fluctuating distances between neighboring cells is found to be a self-similar Weierstrass-Mandelbrot-type function with a nontrivial scaling exponent. The relationship among the quantities describing the distribution is discussed in terms of a balance between a deterministic multiplicative and a stochastic additive process, described by a Perron-Frobenius operator. Two regions of the Kohonen learning parameter α, separated by ${\mathrm{\alpha }}_{\mathit{c}}$≊0.63, differ in the character of both fluctuation and ordering, the latter being fastest close to ${\mathrm{\alpha }}_{\mathit{c}}$.