Recent experiments show that above-threshold ionization (ATI) with intense linearly polarized light occurs via Stark-shifted bound-state resonances. Under identical conditions, we find that ATI with subpicosecond circularly polarized light is nonresonant. Unlike longer-pulse experiments, these spectra directly show the ionization rate versus intensity, and can therefore test ATI theories without deconvolving the inhomogeneous laser focus. Keldysh-Faisal-Reiss calculations do not agree with these new experimental results.

Photoelectrons were produced from a gold surface using strong picosecond Nd:glass laser pulses of ${10}^{10}$-W/${\mathrm{cm}}^2$ intensity. Unexpectedly high (up to 600 eV) energies were observed in the electron energy spectrum only when space-charge effects were completely eliminated. This result is compared with the well-known electron energy spectra of the multiphoton ionization of gases.

This paper proposes a microscopic model for the continuous measurement of photon numbers where the continuous measurement is simulated by a sequence of infinitesimal processes. Each process is composed of a unitary evolution for the coupled system, which consists of the field and the measuring apparatus, followed by a projection according to the readout of the measuring apparatus. The proposed model consists of two-level atoms that are coupled one by one with an optical cavity field via the electric-dipole interaction. Each atomic level is then read out after the interaction, causing a nonunitary state reduction of the field. In particular, it is shown that this microscopic model leads to the Srinivas-Davies model that has been postulated for the photodetection process.

We have demonstrated the detection of weak optical signals via the decay of an unstable state. A Q-switched laser is an example of an unstable state, the decay of which has to be triggered either by quantum fluctuations or by an injected external signal. Measurement of the initiation time of the laser intensity allows us to determine the strength of the external signal with a dynamic range of 7 orders of magnitude. It is possible to detect signal levels that correspond to less than one photon in a selected cavity mode.

The characteristic function method is used to obtain the diffusion tensor for symplectic maps. At lowest order the quasilinear result is obtained, and a series in higher-order correlations is developed. Comparison of the theory to numerical experiments is given using a four-dimensional example of Froeschlé. The experiments agree well with the theory for moderately large parameters. Arnol’d diffusion for the ‘‘thick-layer’’ case is discussed. It is shown that the short-time correlations in one canonical plane affect the diffusion in the other plane even in the limit of zero coupling. Accelerator modes exist for the Froeschlé example and cause divergences in the diffusion, but these only appear when the accelerating region is included in the ensemble.

We present a method that allows one to decide whether an apparently chaotic time series has been filtered or not. For the case of a filtered time series we show that the parameters of the unknown filter can be extracted from the time series, and thereby we are able to reconstruct the original time series. It is demonstrated that our method works and provides reliable values of the fractal dimensions for systems that are described by maps or differential equations and for real experimental data.

We calculate, by performing a product of random matrices, the specific heat and its derivative for the problem of directed polymers in a random medium. Our results are consistent with the existence of a phase transition both in 3+1 and 2+1 dimensions and with the absence of a phase transition in 1+1 dimensions. Our finite-size scaling analysis leads to α=-0.1±0.1 in 3+1 and α=-1.0±0.2 in 2+1 dimensions.

A generalized Emden equation is shown to appear in the description of a wide variety of critical systems as a reduced equation for multidimensional kinetic equations for the order parameter. We have surveyed some of the known solutions and found a number of types of physical behavior such as singular, decaying, and oscillatory damped. A new method of finding appropriate solutions has been given together with, in some cases, severe restrictions on its use. An important link between a generalized Emden equation and an autonomous equation for a damped anharmonic oscillator has been found and exploited.

The dynamics of domains and domain walls in spatially one-dimensional systems is investigated for the case that the evolution equation contains nonweighted spatial averages of the order parameter or a function of it (strongly nonlocal dynamics). Two ordinary differential equations for reduced order parameters are introduced. The first one governs the dynamics of domain states and domain-wall positions. For large systems, there occurs a separation of time scales that leads to a second reduced equation of motion governing the dynamics of the domain sizes. The time scale of the domain-size dynamics is proportional to the length of the system. Validity conditions of both reduced equations of motion are discussed. The ballast resistor and another current instability system serve as illustrations.

A number of stochastic models of two-dimensional crystal growth or evaporation are considered. They are based on the terrace-ledge-kink picture of a crystal surface and are restricted to the growth of a crystal with rectangular symmetry from a gas or dilute solution at close to equilibrium conditions. One of the cases leads to a growth equation for the interface that can be transformed to Burgers’s equation, allowing an exact analysis of the basic growth properties.

We have studied a class of dynamical models exhibiting self-organized criticality, which have recently been introduced by Bak, Tang, and Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987)] by the Monte Carlo renormalization-group (MCRG) technique. In particular, we estimate critical exponents for the ‘‘sandpile’’ model in dimensions d=2 and 3 by MCRG, and present numerical simulations for d=4, which is thought to be the upper critical dimension. Our results are to higher precision than, although consistent with, the original numerical work on the problem. We further compare our results to those of a recent conjecture.

The geometry of a random dense packing of disks of equal size obtained by compacting a random sequential adsorption configuration is discussed. The configuration is shown to be without any long-ranged order, and no local configurations of ordered domains were found. The fraction of area covered by disks is θ=0.772±0.002, and the number of contacts per disk are 3.02±0.03. It is argued that this random packing is a stable configuration close to the random loose-packed limit in two dimensions. The packing fraction of the compacted packing is close to a prediction we make of θ=0.78 for a random loose-packed configuration. Several statistical distributions calculated from the limiting geometry is studied. Both the area and circumference distributions of the Voronoi-Dirichlet polygons could be fitted to Γ distribution functions.

Methods of statistical physics are used to study properties of a one-dimensional lattice of coupled tent maps as a model for spatiotemporal intermittency. Ensemble-averaged quantities are calculated from a large number of random initial values. In a coarse-grained description, the dynamical phase transition that occurs in the model can be characterized as a directed percolation process. Two approximations of mean-field type are introduced. The first method assumes a uniform probability density for the steady-state distribution of phase-space variables. In the second method, this invariant probability measure is calculated self-consistently. The mean-field predictions are compared to direct numerical iterations of finite lattices. The critical behavior is characterized by finite-size scaling expressions that allow us to extract critical exponents from small lattices. The scaling indices depend on the parameters of the model.

A mechanism is presented and analyzed that accomplishes the unification of a number of experimentally observed one-parameter sequences of dynamical behavior as parts of a continuous spectrum that ranges from the U sequence to Farey sequences. Farey sequences, by which we mean one-parameter sequences whose periodic windows correspond to Farey series of rational numbers, have generally been associated with motion on a state-space torus. The mechanism analyzed here does not involve a torus.

The equilibrium thermodynamics of a many-particle assembly in the presence of an external scalar field is examined. Two types of scalar coupling are considered: an external field coupled to the particle density and an external scalar field coupled to the energy density. It is shown that the broken translational and rotational invariance of the system due to the external field is reflected in the macroscopic physics by loss of the usual extensivity property of the system and by means of anisotropy in the response of the system to changes in the system lengths or to the system shape. In addition, the assumptions used in local equilibrium analyses are shown to be incorrect in principle. Nonlocal effects due to the external field must be included in the determination of the equation of state. Simple model calculations for a system in an external gravitational field and an externally imposed temperature field are presented as illustrations.

We analyze within a mean-field approach the stationary states of the kinetic Ising model described by the Glauber stochastic dynamics and subject to a time-dependent oscillating external field. We have found that the magnetization of the system oscillates in time around a certain value that is zero at high temperatures or large field amplitudes and nonzero at low temperatures and small field amplitudes. The transition from one regime to the other, which corresponds to a spontaneous symmetry breaking, is found to be continuous for sufficiently small values of the field amplitudes. For higher values the transition becomes discontinuous and the system exhibits a dynamical tricritical point.

The term stochastic resonance has been adopted to describe an interesting statistical property of periodically modulated and noise-driven multistable dynamical systems: Under the proper conditions, an increase in the input noise level results in an increase in the output signal-to-noise ratio. That is, increasing the disorder of the input leads to increasing the order of the output. This curious phenomenon was first introduced as a possible explanation of the observed periodicity in the recurrences of the earth’s ice ages. The phenomenon is, however, observable in a variety of devices ranging from lasers to electronic circuits. We present here the results of some analog simulations based on the simplest generic nonlinearity: the quartic bistable potential modulated with an additive sinusoidal function. These results are compared to recent theories where available. Special features of the power spectrum are observed, which are predicted by some but not all theories, and which are observed also in recent laser experiments. In addition to measurements of the power spectrum, upon which nearly all previous studies have been based, we introduce precision measurements of the probability density of residence times for which no nonadiabatic theory exists.

Consider an isolated statistical system specified by a coordinate x and its probability density p(x). A functional of p(x) called ‘‘Fisher information’’ can be used to measure the degree of disorder of the system due to the spread in p(x). Fisher information may be minimized, subject to a physical constraint, to attain a temporal equilibrium solution p(x). When the constraint is linear in the mean kinetic energy of the system, the equilibrium solution p(x) often obeys the correct differential equation for the system. In this way, the Schrödinger (energy) wave equation, Klein-Gordon equation, Helmholtz wave equation, diffusion equation, Boltzmann law, and Maxwell-Boltzmann law may be derived from one classical principle of disorder. The convergence rate for Fisher information is about that for alternative use of maximum entropy (in problems where both have the same equilibrium solution). This suggests that Fisher information defines an arrow of time. The arrow points in the direction of decreasing accuracy for the determination of the mean, or ideal, value of a parameter.

We report simulations of the velocity autocorrelation function (VACF) of a tagged particle in two- and three-dimensional lattice-gas cellular automata, using a new technique that is about a million times more efficient than the conventional techniques. The simulations clearly show the algebraic ${\mathit{t}}^{\mathrm{-}\mathit{D}/2\mathrm{}}$ tail of the VACF. We compare the observed long-time tail with the predictions of mode-coupling theory. In three dimensions, the amplitude of this tail is found to agree within the (small) statistical error with these predictions. In two dimensions small but significant deviations from mode-coupling theory of up to 5% are observed.

We present a thermodynamic formalism incorporating the exponential dimension that was proposed to take proper account of the contribution of the harmonic lengths (i.e., lengths that go inversely with n, the stage of refinement of the set of interest). This behavior can be observed in sets such as the Julia set and the irrational windings of the circle map. We obtain the form of the free energy for such sets and find that it has terms proportional to n and lnn, in agreement with the previous numerical estimates for the Julia set. We formulate an inversion procedure capable of exposing the n dependence of the scaling functions of a given set from the knowledge of its exponential and generalized dimensions and show that it gives the correct dependence for known sets.