We study the existence or nonexistence of true trajectories of chaotic dynamical systems that lie close to computer-generated trajectories. The nonexistence of such shadowing trajectories is caused by finite-time Lyapunov exponents of the system fluctuating about zero. A dynamical mechanism of the unshadowability is explained through a theoretical model and identified in simulations of a typical physical system. The problem of fluctuating Lyapunov exponents is expected to be common in simulations of higher-dimensional systems.

We present an exact analytic solution to describe the quantum dynamics of the vacuum field coupled with an oscillating boundary (mirror) in a one-dimensional cavity. We show that the finite part of the field energy density grows in the form of two traveling wave packets which become narrower as time increases. We also discover a "sub-Casimir" region where the energy density can be even smaller than the corresponding static vacuum value.

The use of chaos to transmit information is demonstrated experimentally. The symbolic dynamics of a chaotic electrical oscillator is controlled to carry a prescribed message by use of extremely small perturbing current pulses.

Semiconductor microdisk laser linewidths are measured for cavity volumes near a cubic wavelength. The linewidths remain near the subthreshold values for pump powers well above threshold in agreement with a microscopic theory that includes the coupled dynamics of the optical emission and the nonequilibrium electron-hole gas in the cavity.

We study the effect of near dipole-dipole interactions on the electric susceptibility of a coherently prepared three-level $\Lambda$ system. We discuss the influence of atomic nonlinearities on the recently predicted enhancement of the absorptionless index of refraction and inversionless gain due to local field effects [J.P. Dowling and C.M. Bowden, Phys. Rev. Lett. 70 1421 1993] and predict a density dependent, or piezophotonic, switching between absorption and amplification.

The effect of an acoustic wave packet falling onto a thin 3D filament of vorticity is identified and analyzed. The wavelength of sound decreases to zero in a finite time in such a process. Therefore, even if viscosity is small the wave packets will reach the scales of strong viscous dissipation and get absorbed, transferring their energy to the thermal energy of the compressible vortex flow. The cross section of the sound absorption by multiple vortex filaments having an arbitrary 3D shape is derived. Applications to the theory of the second sound attenuation in He II are discussed.

Quantum suppression of diffusion on stochastic webs is shown to take place for the kicked harmonic oscillator in the form of exactly periodic recurrences. This phenomenon occurs, in general, only if three conditions are satisfied: (1) The kicking potential is odd, up to an additive constant. (2) The web is crystalline with square or hexagonal symmetry. (3) A dimensionless $h$ assumes integer values. The nature of the phenomenon and its sensitivity to small perturbations are examined in terms of generalized kicked Harper models and the theory of topological Chern invariants.

A general method to construct wave functions highly localized on a given periodic orbit, using the information contained in the short term quantum dynamics of the system, is presented. The relationship with the Husimi's quasiprobability distribution in phase space is also discussed.

We report wave dispersed optical third harmonic generation (THG) studied in the fundamental wavelength range of 0.8-1.9 μm in thin films of ${\mathrm{C}}_{70}$. The THG spectrum shows a broad resonance enhancement in cubic susceptibility ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ with a maximum value of ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}(-3\mathrm{}\omega ;\omega ,\omega ,\omega )=(0.9\mathrm{}\pm 0.1)\times {10}^{-10\mathrm{}}$ esu located at 1.42 μm, and a dramatic decrease at higher energies. We interpret the data in terms of a three-level model consisting of a totally symmetric ground state, along with two excited states: a one-photon state and a two-photon state. We predict the presence of a low-lying dipole-forbidden electronic level in close proximity to a dipole-allowed level.

A random matrix ensemble incorporating both Gaussian unitary ensemble and Poisson level statistics while respecting $U\left(N\right)\mathrm{}$ invariance is proposed and shown to be equivalent to a system of noninteracting, confined, one-dimensional fermions at finite temperature.

Two-dimensional system modeling a central region in an experimental box on the basis of the Boussinesq approximation is examined numerically. It is assumed that the effect of mixing and boundary layers on the central region is taken into account only as a forcing to the temperature dynamics. Neutrally stable stratification and homogeneity are also assumed. Entropy ($T^2$) spectra are compared with ones obtained by experiments. It is shown that smaller scales are governed by the entropy cascade process and large-scale modes are induced through the energy inverse transfer.

We discuss fingerprints of classical chaos in spectra of the corresponding bound quantum systems. A novel quantity to measure quantum chaos in spectra is proposed and a conjecture about its universal statistical behavior is put forward. Numerical as well as theoretical evidence is provided in favor of the conjecture.

We compute the dispersion laws of chaotic periodic systems using the semiclassical periodic orbit theory to approximate the trace of the powers of the evolution operator. Aside from the usual real trajectories, we also include complex orbits. These turn out to be fundamental for a proper description of the band structure since they incorporate conduction processes through tunneling mechanisms. The results obtained, illustrated with the kicked-Harper model, are in excellent agreement with numerical simulations, even in the extreme quantum regime.

We show how to use topological analysis to construct from experimental data a symbolic coding of a chaotic attractor. Time series data from a chaotic ${\mathrm{CO}}_2$ laser with modulated losses operating within parameter regions corresponding to attractor crises have been analyzed. A procedure for determining a generating partition from the data is presented, and the connection between crises and a symbolic description of the dynamics is determined.

We numerically investigate nonlinear propagation of ultrashort pulses in a one-dimensional photonic band gap structure. We find that, near the band edge, nonlinear effects cause a dynamical shift in the location of the band gap. We demonstrate that this nonlinear mechanism can induce intensity-dependent pulse transmission and reflections. In addition, pulse reshaping and pulse generation is observed. This phenomenon has important new applications in both optical limiting and optical switching.

Behavior of a falling paper in a two-dimensional fluid is investigated by introducing a simple phenomenological model including the lift and friction terms. Five falling patterns are discovered with the increase of friction coefficients: periodic rotation, chaotic rotation, chaotic fluttering, periodic fluttering, and simple perpendicular fall. Irregular motions of the fall are explained in terms of low-dimensional chaos.

We predict multifrequency $2\pi$ solitons in the cascade stimulated Raman scattering, mode locked by the dynamics of Raman quantum transition; they are "eigensolitons" of a general solitary wave solution. Soliton components at each individual frequency are "bright" pulses of the same, Lorentzian, shape; their interference gives rise to the train of well resolved high intensity subfemtosecond pulses.

Continuity on an embedded phase space is enough to imply determinism in time series. Also, it is possible to define infinitely many arbitrary vector fields over an attractor. We exploit this arbitrariness to generate a detector of smoothness and therefore of determinism in time series. We report results of numerical studies of both flow and map examples and of a chaotic experimental system.

We observe on-off intermittency in a nonlinear electronic circuit tuned near a Hopf bifurcation point. The circuit is driven randomly through the bifurcation point, resulting in intermittent switching between a fixed point (laminar phase) and a limit cycle. The distribution of lengths of laminar phases exhibits -3/2 power law scaling for shorter phases, and an exponential drop for longer phases, due to noise in the system. These results agree with a theoretically predicted distribution. In addition, the crossover from power law to exponential decay obeys the predicted scaling law.

In a laser with delayed feedback operating in an oscillatory regime, phase defects appear for delays longer than the oscillation period. These defects are visualized by rearranging the data in a two-dimensional representation. Two distinct disordered phases are observed, one of weak turbulence characterized by phase fluctuations, and one of highly developed turbulence characterized by a constant density of defects. The transition between the two regimes is analyzed by studying the dependence of the defect lifetime on the delay. The experimental findings are modeled via a generalized Landau equation which includes a delayed coupling.