Excitation and fluorescence spectra of the HgZn excimer were observed in a mixture of Hg and Zn vapors contained in a quartz cell and subjected to pump-and-probe pulsed-laser excitation. The excitation spectrum extended from about 6600 Å to over 8000 Å; in the 6900–7700-Å region it exhibited some structure, but elsewhere it appeared to be structureless. The fluorescence spectrum was recorded in the 2600–2750-Å region and appeared as a series of Condon diffraction patterns arising from the bound-free decays of various vibronic states to the repulsive ground state. We believe the excitation spectrum to arise from B$0^{+}$←A1 vibronic transitions and the fluorescence spectrum from B$0^{+}$→X$0^{+}$ transitions.

The quantized electromagnetic field in interaction with nonrelativistic sources, i.e., atoms and molcules, has been the subject of study in the previous papers in this series. The Heisenberg formalism is used to calculate the electric- and magnetic-field operators arising from charges and currents expressed in multipolar form. In this paper, quadratic operators in these fields such as the Thompson energy density and the Poynting vector and their expectation values for specified states are found. The expectation values are, in general, time dependent. For initial conditions given at t=0 it is shown that the fields are causal, i.e., for t<r/c the source-dependent fields are zero and the quadratic operators have only their zero-point contributions. For t>r/c they have both time-independent and time-dependent terms. The time-dependent terms, though transient, are shown to obey Poynting’s theorem. The steady-state part of the Poynting vector is related to the Einstein coefficients. The corresponding electric-energy density is related to the Casimir-Polder potential for a polarizable test body in the field of the source molecules. Similarly the magnetic-energy density is derived and is used in the calculation of energy shifts. Quadratic operators referring to different field points are also discussed.

By using a self-consistent projection-operator method, developed recently by the author, finite-time deviations from exponential decay for the Lyman-α radiation in the Dirac hydrogen atom are calculated without neglecting retardation and virtual-transition effects.

The after-saturation free-induction-decay (FID) rate of an electron spin transition has been measured in a dilute ruby sample, and a marked departure from the Bloch-like behavior has been found. The similarity with the results obtained recently by Szabo and Muramoto [Phys. Rev. A 39, 3992 (1989)] in the same system but for optical FID points out the close link between the non-Bloch behavior of the FID emission observed in optics and in magnetic-resonance systems. Our results are compared with the theoretical predictions of a statistical theory of the FID emission, but poor agreement is found.

Employing the model of a pulsed Morse oscillator, we show that adiabatic evolution of Floquet states is possible even if the quasienergy spectrum is continuous. This fact is of fundamental importance for a mechanism that allows the selective excitation of molecular vibrational states by appropriately shaped, short, strong laser pulses.

Numerical calculations have been performed with real-symmetric and complex-Hermitian matrices of dimension N having nonzero random matrix elements within a relatively narrow band of width M. It is shown that if the ratio M/N is held fixed as the matrix dimension N increases, a sequence of n eigenvalues will exhibit statistical behavior in good agreement with the predicted statistical behavior of the eigenvalues associated with the Gaussian orthogonal and the Gaussian unitary ensembles of random-matrix theory.

Considering the Selberg trace formula as an exact version of Gutzwiller’s semiclassical periodic-orbit theory in the case of the free motion on compact Riemann surfaces with constant negative curvature (Hadamard-Gutzwiller model), we study two complementary basic problems in quantum chaology: the computation of the classical staircase N(l), the number of periodic orbits with length shorter than l, in terms of the quantal energy spectrum {${\mathit{E}}_{\mathit{n}}$}; the computation of the spectral staircase scrN(E), the number of quantal energies below the energy E, in terms of the length spectrum {${\mathit{l}}_{\mathit{n}}$} of the classical periodic orbits. A formulation of the periodic-orbit theory is presented that is intrinsically unsmoothed, but for which an effective smoothing arises from the limited ‘‘input data,’’ i.e., from the limited knowledge of the periodic orbits in the case of scrN(E) and the limited knowledge of quantal energies in the case of N(l). Based on the periodic-orbit formula for scrN(E), we propose a rule for quantizing chaos, which simply states that the quantal energies are determined by the zeros of the function ${\xi }_1$(E)=cos[πscrN(E)]. The formulas for N(l) and scrN(E) as well as the quantization condition are tested numerically. Furthermore, it is shown that the staircase scrN(E) computed from the length spectrum yields (up to a constant) a good description of the spectral rigidity ${\mathrm{\Delta }}_3$(L), and thus we are able to compute a statistical property of the quantal energy spectrum of a chaotic system from classical periodic orbits.

The parametrically damped pendulum exhibits chaotic transients over a sizable portion of its state space. Using the techniques of interpolated cell mapping (ICM), it has been found that these transients arise from the spatial congruence of the basin of attraction of a stable stationary solution and the remnant of a destroyed strange attractor. The mean transient lifetime is found to scale as ‖ε-${\mathrm{\epsilon }}_{\mathit{c}}$${\mathrm{\Vert }}^{\mathrm{-}\gamma }$, where ε is a system control parameter, ${\mathrm{\epsilon }}_{\mathit{c}}$ is its value at the chaotic boundary, and γ is the critical exponent. Also included are ICM data that reveal the nature of basin transformations as nonchaotic boundaries in the state diagram are traversed.

A higher-order algorithm for the numerical integration of one-variable, additive, white-noise equations is developed. The method of development is to extend standard deterministic Runge-Kutta algorithms to include stochastic terms. The ability of the algorithm to generate proper correlation properties is tested on the Ornstein-Uhlenbeck process, showing higher accuracy even with longer step size.

Both a second-order and a fourth-order stochastic extension of standard Runge-Kutta algorithms are developed for colored-noise equations. These algorithms are tested by computing mean first-passage times in a bistable potential driven by colored noise.

We study the effective shear and bulk moduli of a solid suspension of spheres with a spherically symmetric elastic profile. A mean-field approximation is derived which corresponds to the Lorentz local field in the theory of dielectrics. Thus the approximate expressions for the effective shear and bulk moduli are the analogs of the Clausius-Mossotti equation for the effective dielectric constant. For the case of uniform spheres the expressions are closely related to the Hashin-Shtrikman bounds. We show that the mean-field expression may be corrected systematically for correlations in the sphere positions on the basis of cluster expansions derived by statistical methods.

We consider a system of particles on a lattice of L sites, set on a circle, evolving according to the asymmetric simple-exclusion process, i.e., particles jump independently to empty neighboring sites on the right (left) with rate p (rate 1-p), 1/2<p≤1. We study the nonequilibrium stationary states of the system, when the translation invariance is broken by the insertion of a blockage between (say) sites L and 1; this reduces the rates at which particles jump across the bond by a factor r, 0<r<1. For fixed overall density ${\mathrm{\rho }}_{\mathrm{avg}}$ and r≲(1-‖2${\mathrm{\rho }}_{\mathrm{avg}}$-1‖)/(1+‖2${\mathrm{\rho }}_{\mathrm{avg}}$-1‖), this causes the system to segregate into two regions with densities ${\mathrm{\rho }}_1$ and ${\mathrm{\rho }}_2$=1-${\mathrm{\rho }}_1$, where the densities depend only on r and p, with the two regions separated by a well-defined sharp interface. This corresponds to the shock front described macroscopically in a uniform system by the Burgers equation. We find that fluctuations of the shock position about its average value grow like ${\mathit{L}}^{1/2}$ or ${\mathit{L}}^{1/3}$, depending upon whether particle-hole symmetry exists. This corresponds to the growth in time of ${\mathit{t}}^{1/2}$ and ${\mathit{t}}^{1/3}$ of the displacement of a shock front from the position predicted by the solution of the Burgers equation in a system without a blockage and provides an alternative method for studying such fluctuations.

We study the chaos for a set of coupled, nonlinear partial-differential equations that originate from the equation of motion and the Fourier transform of the mass-conservation equation for the Malkus waterwheel. Dissipation for this system is produced by an adjustable brake. The braking force, proportional to the angular velocity of the wheel, is responsible for the appearance of chaos. The variation of the moment of inertia with time is taken into account. In the large-time limit, the moment of inertia of the composite system, consisting of the wheel and water, tends to a constant, and the three controlling equations of the set of coupled limit equations reduce to a special case of the Lorenz equations, in which the Rayleigh number ρ (here characterizing the distribution of water inflow along the perimeter of the wheel) can also assume negative values. Chaotic attractors of the higher harmonics of the water density have been investigated. Boundaries between various regimes of the wheel’s limit behavior (uniform rotation, periodic reversals of spin, chaotic reversals) in the Lorenz parameter space have been found. The Lorenz parameter space has thus been explored in considerably more detail than by previous authors.

We present accurate estimates for the prefactors of the second and third moments of the height and free-energy fluctuations, as well as the leading correction to the growth rate and free energy per unit length, obtained from extensive simulations of a wide range of one-dimensional models of growing interfaces and directed polymers in a random environment. When scaled by the appropriate model-dependent parameters the amplitudes reduce to universal numbers which characterize the strong-coupling fixed point of the equation of Kardar, Parisi, and Zhang [Phys. Rev. Lett. 56, 889 (1986)]. To check the expected scaling we use models for which the model parameters can be computed analytically. For other systems, such as ballistic deposition, the restricted solid-on-solid model, and the finite-temperature directed polymer, the parameters are determined numerically from steady-state properties. Apart from the standard transient simulation which starts from a flat interface, we also report results for time-dependent correlations in the steady state, which give rise to different universal amplitudes. We compare our results with recent predictions arising from replica calculations and dynamic renormalization-group treatments, finding agreement in the latter but severe discrepancies in the former case. We speculate that the failure of replica theory may be indicative of replica symmetry breaking.

We investigate the dynamics of the second-order moments of wave packets by means of density-matrix techniques. In particular, we consider the existence of shape-conserving pure states and ensembles.

Mandelbrot’s rule for sections is generalized to apply to the Hentschel and Procaccia fractal dimension at arbitrary q and on arbitrary sections. It is shown that for almost all (n-m)-dimensional sections, ${\mathit{D}}^{\mathit{n}}$(q)=${\mathit{D}}^{\mathit{n}\mathrm{-}\mathit{m}}$(q)+m, where the ${\mathit{D}}^{\mathit{r}}$(q) are box-counting, Hentschel, and Procaccia generalized fractal dimensions of r-dimensional sections of homogeneous fractal point sets in ${\mathit{R}}^{\mathit{n}}$ and ${\mathit{D}}^{\mathit{n}\mathrm{-}\mathit{m}}$(q)>0. The rule applies for finite ‘‘thickness’’ sections as well as ‘‘true’’ sections and can be interpreted for inhomogenous fractal sets.

We study the dynamics of a three-dimensional system with a nonconserved complex order parameter Ψ(r,t), following a quench below the ordering transition temperature. For a critical quench [〈Ψ(r,0)〉=0] we observe dynamical scaling and an effective value of the dynamical exponent of φ=0.45±0.01. For an off-critical quench [〈Ψ(r,0)〉≠0] there is a breakdown of dynamical scaling and the vortex-string length l(t) varies with time t as l(t)∼${\mathit{t}}^{\mathrm{-}1}$exp(-γ${\mathit{t}}^{3/2}$), in good agreement with a theoretical calculation by Toyoki and Honda. The predicted relation γ∝‖〈Ψ(r,0)〉${\mathrm{\Vert }}^2$ is found to represent only a lower bound. We indicate the possible relevance of these results for liquid-crystal systems and cosmological pattern formation.

We present a sandpile cellular-automata model that includes the effects of inertia. The model is studied in both one and two dimensions. We find that the model changes the normal self-organized critical behavior, creating a dominance of big events in the system and leading to very large fluctuations in the mass of the system. We show that those changes of behavior can only be noticed in large sandpiles, which is in accord with previous experimental results.

We introduce the correlation length for the square-tiling model for the glass transition through the transfer-matrix approach developed earlier [S. M. Bhattacharjee and E. Helfand, Phys. Rev. A 36, 3332 (1987)] for this model. We show that this transfer-matrix approach, in the limit when the competing internal energy reduces the model to the hard-square gas problem with nearest- and next-nearest-neighbor exclusion, is equivalent to the conventional row-to-row transfer matrix. Based on this, we propose that the transitions for other values of the coupling constant for the competing term are also nonuniversal, as is known for the hard-square gas problem.

The transition regime from periodic and quasiperiodic motion to spatiotemporal chaos is examined for coupled-map lattices. For periodic states the stability criteria for homogeneous solutions are determined, and the formation of checkerboard patterns is treated analytically. Also, the period-doubling route to spatiotemporal chaos is discussed. For the quasiperiodic transition, renormalization-group analysis is carried out for both forward coupling and the more generic linear coupling. This leads to scaling results for the spatiotemporal intermittent regime. In particular, a coherence length is identified, based on the distributions of the phase fluctuations and their derivatives. Finally, percolation methods in the study of spatiotemporal intermittency are numerically tested. It is shown that finite-size effects are substantial.