A small change of one of the system parameters may not in general convert a bistable system to a monostable system. However, an external control in the form of a slow periodic parameter modulation can annihilate one of the coexisting states, and thus results in controlled monostability. The annihilation takes place because the state becomes chaotic via the period doubling route and the chaotic state undergoes boundary crisis within a small range of the control amplitude. These features are observed theoretically in two standard models, namely, Hénon map and laser rate equations, and confirmed experimentally in a cavity loss modulated ${\mathrm{CO}}_2$ laser.

We present the first quantum system where Anderson localization is completely described within periodic-orbit theory. The model is a quantum graph analogous to an aperiodic Kronig-Penney model in one dimension. The exact expression for the probability to return to an initially localized state is computed in terms of classical trajectories. It saturates to a finite value due to localization, while the diagonal approximation decays diffusively. Our theory is based on the identification of families of isometric orbits. The coherent periodic-orbit sums within these families, and the summation over all families, are performed analytically using advanced combinatorial methods.

Tunneling of photons in frustrated total internal reflection has been studied in the time domain with single-cycle femtosecond pulses. It is seen that both the phase and energy of the pulse travel faster than the speed of light in vacuum. Theoretical analysis of the experiments shows that the time-response function for electromagnetic waves propagating in the air gap is noncausal. However, it is found that superluminal signal propagation is not possible in this case because of the inevitable diffractive spreading of the signal beam.

Single and multiple scattering of light by magnetic particles and their implications to the coherent backscattering effect are reported. Single scattering of light by small magnetic particles presents unusual features such as forward-backward asymmetry and resonance effects. In multiple scattering, this leads to a global decrease in the localization parameter $k{\ell }^{*}$, which exhibits an oscillatory dependence on the scatterer magnetic permeability. By considering magnetic scatterers following a Curie-Weiss susceptibility law, we suggest that $k{\ell }^{*}$ can be tuned by varying the temperature.

We present precise and reproducible mean pressure measurements at the bottom of a cylindrical granular column. If a constant overload is added, the pressure is linear in overload and nonmonotonic in the column height. The results are quantitatively consistent with a local, linear relation between stress components, as was recently proposed by some of us. They contradict the simplest classical (Janssen) approximation, and may rather severely test competing models.

Experiments have found that freely relaxing turbulence in inviscid, incompressible two-dimensional Euler flows can self-organize into ordered structures—vortex crystals—in which a number $N_c\sim 2–20$ of strong vortices form stable, rigidly rotating patterns in a low vorticity background. In this paper we show that $N_c$ can be roughly predicted from properties of the flows in the early stage of the turbulent relaxation.

We derive a fully nonlinear evolution equation that can describe the two-dimensional motion of finite-amplitude long internal waves in a uniformly stratified three-dimensional fluid of finite depth. The derived equation is the two-dimensional counterpart of the evolution equation obtained by Grimshaw and Yi [J. Fluid Mech. 229, 603 (1991)]. In the small-amplitude limit, our equation is reduced to the celebrated Kadomtsev-Petviashvili equation.

Fundamental limits on the controllability of physical systems are discussed in the light of information theory. It is shown that the second law of thermodynamics, when generalized to include information, sets absolute limits to the minimum amount of dissipation required by open-loop control. In addition, an information-theoretic analysis of control systems shows feedback control to be a zero sum game: each bit of information gathered from a dynamical system by a control device can serve to decrease the entropy of that system by at most one bit additional to the reduction of entropy attainable without such information. Consequences for the control of discrete state systems and chaotic maps are discussed.

We present a method for the statistical analysis of quantum spectra which goes beyond the standard nearest-neighbor spacing distribution. The method exploits a peculiar correlation of oscillator strength and level spacing distributions. For diamagnetic Rydberg spectra we demonstrate that core-induced chaos and generic chaos can be distinguished in an experimentally accessible regime far below the semiclassical limit and with already a few hundred lines per spectrum. We present two hypotheses for a generalization of our findings.

We propose composite solitons carrying topological charge: multicomponent two dimensional [ $(2+1)\mathrm{D}$] vector (Manakov-like) solitons for which at least one component carries topological charge. These multimode solitons can have a single hump or exhibit a multihump structure. The “spin” carried by these multimode composite solitons suggests $3\mathrm{D}$ soliton interactions in which the particlelike behavior includes spin, in addition to effective mass, linear, and angular momenta.

In this Letter, we investigate the behavior of the cholesteric liquid-crystal Fabry-Perot cavity in the spectral range of the Bragg reflection band. We show that in this region the $2\times 2-\mathrm{Jones}-\mathrm{matrix}$ calculation gives a false predication. However, by the use of the $4\times 4-\mathrm{matrix}$ method, interesting features are revealed in the resonance spectra. The resonance spectra split when $\lambda \sim \overline{n}P$. Our experiments confirm this phenomenon. The experimental results show that the splitting occurs in a steplike fashion. This can be explained by the quantization of the pitch that occurs due to the fixed boundary conditions.

Sliding friction between the tip of a friction force microscope and NaCl(100) was studied to deduce the velocity dependence of friction forces on the atomic scale. A logarithmic dependence of the mean friction force is revealed at low velocities. The experimental data are interpreted in terms of a modified Tomlinson model which is based on reaction rate theory.

A field can be specified by a set of spectral coefficients, $\{c_j\left(t\right)\}$, relative to an expansion basis. In fluid turbulence, one often assumes the condition that if one were to extract data from an ensemble of realizations, one would find that the average, $〈c_i^{*}\left(t\right)c_{i^{\prime }}\left(t\right)〉$, would vanish unless ${i=i}^{\prime }$, as in the case of a homogeneous ensemble in which the $i$'s represent wave vectors. We analytically treat an extension to the case in which one has a larger number of coefficients than realizations, introducing intrinsic linear dependences that vitiate the stated condition.

In the 1950s, D'yakov and Kontorovich predicted that under certain conditions perturbed shock waves in nonideal gases can become unstable by emitting undamped sound and entropy-vortex waves. For the last 45 years, though, little progress has been made in the identification and numerical modeling of physical conditions for which this phenomenon might occur. Using a van der Waals equation of state, we present for the first time a dynamical simulation of a D'yakov-Kontorovich instability. The two-dimensional emission pattern of acoustic waves appearing in the simulation agrees with the prediction of a linearized theory.

We report on first experimental signatures for chaos-assisted tunneling in a two-dimensional annular billiard. Measurements of microwave spectra from a superconducting cavity with high frequency resolution are combined with electromagnetic field distributions experimentally determined from a normal conducting twin cavity with high spatial resolution to resolve eigenmodes with properly identified quantum numbers. Distributions of quasidoublet splittings serve as basic observables for the tunneling between whispering gallery-type modes localized to congruent, but distinct tori which are coupled weakly to irregular eigenstates associated with the chaotic region in phase space.

We investigate the nonparametric, pure ac driven dynamics of nonlinear Klein-Gordon solitary waves having an internal mode of frequency ${\Omega }_i$. We show that the strongest resonance arises when the driving frequency $\delta ={\Omega }_i/2$, whereas when $\delta ={\Omega }_i$ the resonance is weaker, disappearing for nonzero damping. At resonance, the dynamics of the kink center of mass becomes chaotic. As we identify the resonance mechanism as an indirect coupling to the internal mode due to its symmetry, we expect similar results for other systems.

We have observed quasinondestructive holographic storage with a continuous-wave laser at $\lambda =532\mathrm{}\mathrm{nm}$ in near-stoichiometric ${\mathrm{LiNbO}}_3$ doped with Tb and Fe. This crystal showed an exceptionally long grating decay time and also exhibited a fast color change upon exposure to ultraviolet (UV) light. It was demonstrated that the grating recorded from the UV-exposed, colored state can be continuously read out over 9 h at a reading intensity as high as $8\mathrm{mW}/{\mathrm{cm}}^2$. In addition, the written grating could be easily erased with UV illumination which returned the crystal back to the original colored state.

A method based on Fourier filtered control signals for stabilization of unstable patterns in a nonlinear optical single feedback system is experimentally realized. The successful stabilization of the homogeneous solution and different stationary periodic patterns far above the pattern forming threshold as well as the elimination of spatiotemporal disorder above a secondary instability has been achieved. The temporal evolution of the control signal verifies the underlying philosophy of noninvasive control that changes only the linear stability of the systems' solution and not the solution itself.

We have measured quasiinstantaneous transverse patterns in a broad aperture laser. Nonordered patterns yielding to boundary determined regular structures in progressive time-integrated recording are observed. The linear analysis and numerical integration of the full Maxwell-Bloch equations allow us to interpret the features of the experiment. We show that this system being far from threshold cannot be fully understood with a perturbative model.

Modulated deep-water 1D Stokes waves are considered experimentally and theoretically. Wave trains are modulated in a controlled fashion and their evolution is recorded. Data from repeated laboratory experiments are reproducible near the wave maker, but diverge away from the wave maker. Numerical integration of a perturbed nonlinear Schrödinger equation and an associated linear spectral problem indicate that under suitable conditions modulated periodic Stokes waves evolve chaotically. Sensitive spectral evolution in the neighborhood of homoclinic manifolds of the unperturbed nonlinear Schrödinger equation is found.