The chaotic dynamics found in globally coupled modulated laser systems have been switched into stable orbits, including antiphase periodic states and clustered states, by an injection-seeding method. Direct assignment to desired factorial periodic orbits has been demonstrated. Self-induced switching among destabilized clustered states (chaotic itinerancy) in the transition process from clustered states to global chaos has also been found.

The V and Ξ types of closed lifetime-broadened systems with lower-level-dressed-state preparation by a strong electromagnetic field are analyzed. It is found that the coherence in dressed states enhances the gain in the former system but reduces gain in the latter. However, we show that, since the dressed states are prepared in lower levels, both systems can lase without population inversion in steady state.

We propose a statistical model of rupture as a mechanism for the occasionally observed marked increase of seismic activity prior to a great earthquake. The physical ingredients of the model are those of geometrical inhomogeneity and viscoelastic creep. We demonstrate that the observed inverse power law for the rate of increase of seismicity before a large earthquake requires no assumptions beyond those of a random featureless distribution of inhomogeneities and a typical power law of creep with exponent m. On the average, the rate of energy release in earthquakes dE/dt before a larg e earthquake that will occur at time ${\mathit{t}}_{\mathit{r}}$ increases with time as (${\mathit{t}}_{\mathit{r}}$-t${)}^{\mathrm{-}\mathrm{\beta }}$, with β decreasing from (t+1) for m=0 to 1 as m increases to infinity; in two dimensions t=1.3 is the percolation-conductance exponent. For large m, which is appropriate for ductile-brittle-fracture laboratory measurements, the value of this exponent is in agreement with observations of the number rate of occurrence of earthquake foreshocks. The exponent β is independent of the amount of initial disorder within a broad interval. The power law is a consequence of the many-body interactions between small cracks formed before an impending large rupture. As a consequence of variations in the initial configuration of inhomogeneities, there are large fluctuations in the rate of energy release dE/dt from system to system, a result also consistent with observations of foreshocks in nature.

We introduce and study an implementation technique of the mean-field dynamic-cluster method for the analysis of lattice models. The technique is characterized by two indices (n,m), where n is the size of the clusters and m denotes their overlap. For some lattice models, we find that the cluster method converges to the exact kinetics with increasing cluster size n, in a conventional way. However, for some other models it is shown that the cluster approximation predicts a phase diagram that is qualitatively incorrect even for large n. A reason for this anomalous behavior is suggested. The effect of different, but physically equivalent, representations of the same lattice model on the quality of the approximation results is also explored.

An experiment is proposed to check the physical reality of a nonequilibrium absolute temperature previously proposed from theoretical grounds in the framework of extended irreversible thermodynamics.

In a series of papers, we have studied pattern dynamics in the Bonhoeffer–van der Pol type reaction-diffusion system which is a coupled set of equations for an activator and an inhibitor and exhibits excitability. We have been concerned mainly with localized motionless solutions in one dimension, which have been shown to be stable when the diffusion constant of the inhibitor is sufficiently large. In this paper, we shall explore how the properties of the system change when we decrease the diffusion constant. It is shown that a motionless localized solution turns out to be unstable in such a situation while a propagating-pulse solution can exist stably. This crossover from the motionless to the pulse solutions does not occur as a clear bifurcation. There is a parameter regime where the two solutions can coexist, and rich variety of dynamical patterns is expected.

We study the classical scattering of a point particle on three- and four-disk billiards. The escape dynamics is investigated using the Ruelle classical resonances obtained as the complex poles of the Ruelle ζ functions. The statistical distributions of the real and imaginary parts of the poles as well as their spacings are numerically calculated. Furthermore, we demonstrate the role played by Ruelle’s resonances in the real-time escape processes of an ensemble of classical particles in these scattering systems.

Using a functional formulation of the Keldysh theory we investigate the time evolution of a dilute Bose gas through the critical point. We determine the critical region of the gas and show that if the system is quenched inside this region, Bose-Einstein condensation is nucleated on a time scale of O(ħ/${\mathit{k}}_{\mathit{B}}$${\mathit{T}}_{\mathit{c}}$) by means of a coherent population of the one-particle ground state. We also examine the subsequent buildup of the condensate density, taking place on a much longer time scale. However, in the experimentally interesting case of spin-polarized atomic hydrogen or cesium it is still short compared to the lifetime of the gas.

We discuss continuous-time sporadic dynamics that are intermediate between regular and random behaviors. A characterization of such processes is provided by a scale-dependent entropic quantity, and is applied to a model of Lévy motion introduced by Klafter, Blumen, and Shlesinger [Phys. Rev. A 35, 3081 (1987)]. The study suggests that sporadicity may be a feature of some physical systems exhibiting anomalous diffusion.

We present a theoretical approach that permits the reproduction of the quantum-thermodynamic properties of a variety of physical systems with many degrees of freedom, over the whole temperature range. The method is based on the introduction of an effective classical Hamiltonian ${\mathit{scrH}}_{\mathit{e}\mathit{f}\mathit{f}}$ , dependent on the Planck constant ħ and on the temperature T=${\mathrm{\beta }}^{\mathrm{-}1}$, by means of which classical-like formulas for the thermodynamic quantities can be written. For instance, the partition function is expressed by the usual phase-space integral of ${\mathit{e}}_{\mathit{e}\mathit{f}\mathit{f}}^{\mathrm{-}\mathrm{\beta }\mathit{s}\mathit{c}\mathit{r}\mathit{H}}$. The effective Hamiltonian is the generalization of a previous effective potential. The latter was obtained in the case of standard Hamiltonians, i.e., with a separated quadratic kinetic energy, and has been successfully used in a number of applications. The starting point of the method is the path-integral expression for the unnormalized density operator, and we exploit Feynman’s idea of classifying paths by the equivalence relation of having the same average phase-space point. The contribution of each class of paths to the density matrix is approximated within a generalized self-consistent harmonic approximation (SCHA). We show that the framework is consistent with the usual SCHA, which, however, only holds at low temperatures, as well as with the semiclassical high-temperature expansion by Wigner and Kirkwood. The practical implementation of the method is made straightforward by a further approximation of low quantum coupling.

We find that the dynamics of certain dc-driven Josephson-junction arrays is peculiarly weak. The neutral stability of splay-phase states is far more common than previously suspected, even if the junctions are not identical. This has significant consequences for applications of these arrays.

A possibility of the occurrence of transient multimodality during a decay of an unstable state is analyzed. For the two discussed classes of systems it is found that the appearance of this phenomenon depends only on the sign of the second nonvanishing derivative of the potential at the unstable point. Thus here the transient multimodality is not a noise-induced phenomenon like that for the evolution from an arbitrary state. A scheme of the classification of dynamical systems based on their transient properties is proposed.

It is known that inverse cascades arise in discontinuous logistic maps [de Sousa Viera and co-workers, Phys. Rev. A 35, 945 (1987); in Universalities in Condensed Matter, edited by R. Jullien, L. Peliti, R. Rammal, and N. Boccara (Springer, New York, 1988); in Disordered Systems and Biological Models, edited by L. Peliti (World Scientific, Singapore, 1989); Europhys. Lett. 9, 119 (1989)]. Here we report on the discovery of direct cascades in such maps. Between any two consecutive terms of an inverse cascade there may or may not occur new cycles. We have discovered two empirical rules for the existence of these new cycles. When they do exist, the periods of the new cycles can be predicted by a rule we have discovered numerically, namely the summation rule, which involves a method of generating terms identical to the way terms of a Farey sequence are generated. By application of the summation rule, it is possible to generate both higher-level direct and inverse cascades which have self-similar structures. Further, the existence of direct cascades can also be explained by the same rule. We discuss the role of the discontinuity of the map in relation to bifurcations. We also mention how the cascades and the summation rule become modified in the chaotic region of the map.

A modulated relaxation oscillator with a finite resetting time is considered. The underlying return map, a combination of a circle map and an inverse circle map, is deduced. Two critical lines, associated with an inflection point and a point of infinite slope in the return map, respectively, divide the parameter space into four regions of qualitatively different behavior. One region is chaotic, as the return map is not invertible. In another region, a gap exists in the return map and only periodic attractors are possible. In a third region, the return map simultaneously is noninvertible and contains a gap, which gives rise to a wide range of nonlinear phenomena. The critical lines are found analytically and the structure of the phase-locked steps is studied.

The mechanical behavior of model two-dimensional materials is investigated by large-scale molecular-dynamics (MD) simulations on a massively parallel computer. Both a pair-potential and a model embedded-atom many-body potential are examined. A parallel MD algorithm is developed to exploit the architecture of the Connection Machine, enabling simulations of greater than ${10}^6$ atoms. Adiabatic expansions and spallation experiments on both perfect crystals and granular solids are performed. It is demonstrated that a uniform adiabatic expansion is a good model for the spallation process. The spall strength is shown to be proportional to the logarithm of the applied strain rate. A dislocation-dynamics model is developed to explain the results, which also leads to predictions for the impact spallation experiments.

A key part of the early thermodynamic work on blackbody radiation by Wien, Stéfan, Boltzmann, Planck, and others involved the thermodynamic behavior of a movable piston sliding in a cylinder containing classical electromagnetic thermal radiation. This early work used only classical physics concepts. Here, this analysis is reinvestigated with the change that the implicit assumption is not made that the thermal radiation spectrum reduces to zero at the temperature T=0. Previous work has shown that this consideration may be an important one to yield agreement, or at least better agreement, between classical physical theory and the actual physical behavior of molecular, atomic, and subatomic systems in nature. Indeed, the present analysis on ‘‘cavity thermodynamics’’ accounts for the thermodynamic behavior of Casimir forces between the walls of the cavity. Using only the traditional thermodynamic definition of T=0, the form of the classical electromagnetic zero-point (ZP) radiation spectrum is deduced. From the second law of thermodynamics, two forms of Wien’s displacement law are obtained and generalized to include the possibility of ZP radiation. The entropy is then explicitly calculated for the parallel-plate case. Also, the limiting situation of high-temperature radiation between the plates and low temperature outside is examined to recover the early analysis by Wien, Planck, and others. Most of the analysis is carried out for two parallel conducting plates bathed in thermal radiation; the Appendix extends this analysis to a rectangular conducting box with a movable interior wall.

Using the Wigner method, it is shown that a classical-like equation of motion for a quasiprobability distribution ${\mathrm{\rho }}_{\mathit{W}}$ can be built up, ∂${\mathrm{\rho }}_{\mathit{W}}$/∂t=(L${\mathrm{^}}_{\mathrm{cl}}$+L${\mathrm{^}}_{\mathrm{QGD}}$)${\mathrm{\rho }}_{\mathit{W}}$, which is rigorously equivalent to the quantum von Neumann–Liouville equation. The operator L${\mathrm{^}}_{\mathrm{cl}}$ is equivalent to integrating classical trajectories, which are then averaged over an initial distribution, broadened so as to fulfill the requirements of the quantum uncertainty principle. It is shown that this operator produces semiclassical chaos and is responsible for quantum irreversibility and the fast growth of quantum uncertainty. Carrying out explicit calculations for a spin-boson Hamiltonian, the joint action of L${\mathrm{^}}_{\mathrm{cl}}$ and L${\mathrm{^}}_{\mathrm{QGD}}$ is illustrated. It is shown that the latter operator L${\mathrm{^}}_{\mathrm{QGD}}$ (where QGD stands for quantum generating diffusion), makes the 1/2-spin system ‘‘remember’’ its quantum nature, and competes with the irreversibility induced by the former operator. Some ambiguous aspects of ‘‘irreversibility’’ and ‘‘growth of quantum fluctuations’’ as indicators of semiclassical chaos are discussed.

Near-separatrix eigenfunctions for the double-well potential are analyzed. These functions are needed for the study of systems with perturbed or slowly varying double-well potentials. The probability density of separatrix eigenfunctions collapses to the classical result (a δ function at the unstable fixed point) logarithmically with the number of quantum states. Matrix elements with respect to this basis are also studied. Unlike the wave functions, the unnormalized matrix elements are nonsingular in the limit of large quantum number.

We introduce a growing self-avoiding walk in three dimensions (3D) that can terminate only by returning to its point of origin. This ‘‘tricolor walk’’ depends on two parameters, p and q, and is a direct generalization of the smart kinetic walk to 3D. Our walk is closely related to percolation with three colors (black, white, and gray): the tricolor walk directly constructs a loop formed by the confluence of a black, a white, and a gray cluster. The parameters p and q are the fraction of sites colored black and white, respectively. We present numerical and analytical evidence that for p=q=1/3, the fractal dimension of the tricolor walk is exactly 2. For p=q<1/3, the walks undergo a percolation transition at p≃0.2915. Our Monte Carlo simulations strongly suggest that this transition is not in the same universality class as the usual percolation transition in 3D. The mean length of the finite walks χ is divergent throughout an extended region of the parameter space.