First, we demonstrate Bell’s theorem, without using inequalities, for an experiment with two particles. Then we show that, if we assume realism and we assume that the ‘‘elements of reality’’ corresponding to Lorentz-invariant observables are themselves Lorentz invariant, we can derive a contradiction with quantum mechanics.

The response of an overdamped bistable system to a weak periodic force in the presence of external noise is investigated using linear-response theory and by analog electronic experiment. It is shown, both theoretically and experimentally, that a phase lag $\phi$ exists between the force and the response, and that $\left|\phi \right|$ passes through a maximum when the noise intensity is tuned through the range where stochastic resonance occurs. These results clarify the interrelation between stochastic resonance and conventional resonance phenomena, and confirm that stochastic resonance can usefully be treated by linear-response theory.

The power-law behavior of the average time between intermittent bursts in the NMR-laser dynamics near a heteroclinic tangency crisis is investigated. Using symbolic-dynamical techniques, new crisis-induced sequences are identified in the strange attractors reconstructed from both experimental and simulated data. Our approach provides a precise criterion for the onset of the attractor widening due to the collision of the stable and the unstable manifold belonging to different unstable periodic orbits. The results show the predictability power of our laser model.

We investigate the chaotic temperature dependence of the renormalized couplings in a short-range Ising spin glass. Some of our analytic and numerical results, obtained by the Migdal-Kadanoff renormalization scheme but argued to have general validity, differ from those of the scaling and droplet theory. First, chaos is present also at and above the critical temperature. Second, between ${\mathit{d}}_{\mathit{l}}$=2.46 (the lower critical dimension) and ${\mathit{d}}_{+}$=3.4, the chaos in the critical region is characterized by a new critical exponent ${\mathrm{\zeta }}_{\mathit{c}}$ that has hitherto escaped attention.

In analogy to squeezing of light, noise in a classical oscillator can be squeezed to reduce amplitude uncertainty. While this can be achieved to some extent in a harmonic oscillator parametrically driven at 2${\mathrm{\omega }}_0$, true amplitude squeezing is possible in anharmonic oscillators, either by driving at 2${\mathrm{\omega }}_0$ or allowing amplitude-dependent dephasing. These techniques can reduce the uncertainty in measurements of the frequency of an oscillator; for example, the thermal uncertainty in the relativistic frequency shift in single ion mass spectroscopy can be reduced by more than a factor of 5.

In this paper we present the first experimental verification that the sensitivity of a chaotic system to small perturbations (the ‘‘butterfly effect’’) can be used to rapidly direct orbits from an arbitrary initial state to an arbitrary accessible desired state.

Wave functions of a stadium billiard are determined in a microwave analog experiment. It is shown that Gutzwiller’s semiclassical representation of the Green’s function in terms of classical trajectories can account not only for eigenvalue spectra but also for eigenfunction patterns.

We consider the overdamped ac-driven dynamics of an incommensurate one-dimensional array of coupled oscillators in a spatially periodic substrate potential (Frenkel-Kontorova model) by means of molecular-dynamics simulations. The ac steady-state trajectories are described by a two-dimensional hull function which, as the strength of the substrate potential varies, undergoes a transition by the breaking of analyticity. This critical behavior is macroscopically observed as the appearance of Shapiro steps in the response function.

A prehistory problem is formulated for large occasional fluctuations in noise-driven systems. It has been studied theoretically and experimentally, thereby illuminating the concept of optimal paths and making it possible to visualize and investigate them. The prehistory probability distribution measured for a white-noise-driven system, taken as an example, is shown to be in agreement with the theory.

We report a numerical study of near-integrable Hamiltonian systems with many degrees of freedom. Recently reported transition phenomena for a coarse discrete sine-Gordon system are reexamined in the near-integrable limit and with the aid of statistical and integrable diagnostics. We show that the critical energy of transition from recurrence to chaotic transport of energy coincides with the onset, in the initial data, of integrable exponential instabilities and associated homoclinic orbits. This Letter aims to tie together classical and recent numerical experiments and theory of lattice instabilities and integrable systems.

We consider polynomials of high degree with random coefficients which appear in the context of ‘‘quantum chaotic’’ dynamics and investigate various conditions under which their roots tend to concentrate near the unit circle in the complex plane. Correlation functions of roots are computed analytically. We also investigate a certain class of random polynomials whose roots cover, in a uniform way, the Riemann sphere. Special emphasis is devoted to the influence of symmmetries.

We analyze a model of globally coupled nonlinear oscillators with randomly distributed frequencies. Twenty-five years ago it was conjectured that, for coupling strengths below a certain threshold, this system would always relax to an incoherent state. We prove this conjecture for the system linearized about the incoherent state, for frequency distributions with compact support. The relaxation is exponentially fast at intermediate times but slower than exponential at long times. The decay mechanism is remarkably similar to Landau damping in plasmas, even though the model was originally inspired by biological rhythms.

It is shown that the breakdown of a global symmetry group to a discrete subgroup can lead to analogs of the Aharonov-Bohm effect. At sufficiently low momentum transfer, the cross section for scattering of a particle with nontrivial ${\mathrm{Z}}_2$ charge off a global vortex is almost equal to (but definitely different from) maximal Aharonov-Bohm scattering; the effect goes away at large momentum transfer. The scattering of a spin-1/2 particle off a magnetic vortex provides an amusing experimentally realizable example.

The scalar version of the Aharonov-Bohm effect predicts a phase shift for de Broglie waves due to the action of a scalar potential in an otherwise field-free (i.e., force-free) region of space. Unlike the more familiar effect due to the magnetic vector potential, the scalar effect has hitherto remained unverified due, presumably, to technical difficulties in electron interferometry. Rather than using electrons acted on by electrostatic potentials, we have performed an analogous interferometry experiment with thermal neutorns subject to pulsed magnetic fields. The expected phase shifts have been observed to a high degree of accuracy.

Analytic reflectionless potentials ${\mathrm{\omega }}^2$(τ) are constructed for the one-dimensional equation ${\mathrm{\epsilon }}^2$${\mathit{d}}^2$q/d${\mathrm{\tau }}^2$+${\mathrm{\omega }}^2$(τ)q=0. Unlike generic potentials which reflect waves with amplitudes of order exp(-1/ε) as ε→0, these potentials have reflection coefficients which are identically 0. It is shown that in the reflectionless case the adiabatic perturbation or iteration does not converge absolutely or terminate at some order. Since exact integrability is less restrictive than having a reflectionless potential, the case studied also shows that integrability does not imply convergence of the approximation methods used.

Generic, deterministic, nonconservative models displaying self-organized criticality are shown to exhibit 1/f noise. The exponent of the power spectrum depends on the level of conservation.

We have demonstrated for the first time that single photons in glass travel at the group velocity, and have observed a novel, nonlocal dispersion-cancellation effect. We used a two-photon interferometer in which a conjugate pair of photons produced in parametric fluorescence travel separate paths and are detected in coincidence after being recombined at a beam splitter. A piece of glass was placed in the path of one of the photons, and a variable delay was adjusted to precisely compensate for it. The single-photon propagation time was thus measured to within approximately 4 fsec.

We demonstrate that instabilities in a Hamiltonian system can occur via deformations that reduce the symmetry of the system. The movement of eigenvalues at an equilibrium point of a family of Hamiltonian systems is constrained by the symmetry type of the system. If deformations of a family change the symmetry type, then instabilities can appear at multiple eigenvalues that produce large amplitude changes in the system dynamics. We illustrate this phenomenon in the context of a low-dimensional Hamiltonian normal form, and then analyze the instability of a vortex filament in a strain field.

The Wigner distribution of the electric fields in a quasimonochromatic light wave is equivalent, in the paraxial approximation, to the cross-spectral density function of the wave. The intensity distribution in a plane may be described as a projection across this Wigner distribution. Three-dimensional intensity information can be used to generate a set of projections from which it is possible to reconstruct the second-order statistics of the partially coherent wave field.

We study the phase space for arrays of coupled Josephson-junction oscillators which have coexisting in-phase and antiphase attractors. Arrays with four or more oscillators have significantly different attracting sets from those with two or three: Continuous families of out-of-phase attractors can exist instead of isolated ones. A new mechanism in the presence of small amplitude noise is proposed to account for the observed transitions among different stable antiphase states, and the rarely observed transitions between an in-phase and an antiphase attractor.