We describe a quantum many-body system undergoing multiple resonant tunneling which exhibits chaotic behavior in numerical simulations of a mean-field approximation. This phenomenon, which has no counterpart in the classical limit, is due to effective nonlinearities in the tunneling process and can be observed in principle with a heterostructure.

We show that the geometrical (Berry) phases discovered in Hamiltonian systems can also be defined as resulting from parallel transportation of vectors for nonlinear dissipative systems with cyclic attractors. If the nonlinear dissipative systems possess a certain kind of asymptotic solution defined in this Letter, the phase and amplitude accumulation of a geometrical type can be defined. Detuned one- and two-photon lasers showing periodic intensity pulsations are taken as examples of such systems.

A cycle expansion for the Lyapunov exponent of a product of random matrices is derived. The formula is nonperturbative and numerically effective, which allows the Lyapunov exponent to be computed to high accuracy. In particular, the free energy and heat capacity are computed for the one-dimensional Ising model with quenched disorder. The formula is derived by using a Bernoulli dynamical system to mimic the randomness.

We study the time evolution of a wave packet in a rapidly varying (in time) random potential. We find that the wave function becomes ‘‘multifractal,’’ i.e., that an infinite number of exponents is needed to describe its evolution. The width of the packet is found to increase as √t , i.e., diffusively. The evolution of the center of mass is compatible with a subdiffusive ${\mathit{t}}^{1/4}$ law.

We investigate the reaction kinetics for systems in which the dynamics of the particles is governed by a Langevin equation with negligible damping, and we find the expressions for the survival probability, residual concentrations, and reaction rates. We discover that the integral in time of the reaction front for d=1 is ${\mathit{t}}^{1\mathrm{-}\mathrm{\beta }}$ exp(-‖x‖/${\mathit{t}}^{\mathrm{\alpha }}$) for both the low- and high-damping limits, and we estimate the exponents α and β in each case.

We construct a partition function of N anyons in a constant external magnetic field and in an external harmonic potential well. From this we find an equation of state for the free anyon gas. The equation of state exhibits quantum behavior when the density of the anyons is of order of 1/N${\lambda }_{\mathit{T}}^2$, where ${\lambda }_{\mathit{T}}$ is the mean thermal wavelength.

Intermittent behavior originating in a point of discontinuity in 1D maps is investigated. Studying the duration of the laminar phase, we find a logarithmic dependence of the average laminar length 〈l〉 on the control parameter ε, in contrast to the three conventional types of intermittency characterized by power-law scaling. Analytical considerations give the relation 〈l〉=log(ε)/log(s)+β (where s is the ‘‘slope’’ at the point of discontinuity). Numerical data obtained from a relaxation oscillator model are in good agreement with these results.

Numerical tests of a novel semiclassical quantization rule are carried out for three strongly chaotic systems: the hyperbolic billiard, Artin’s billiard, and the Hadamard-Gutzwiller model. The results demonstrate that this novel rule is very effective and capable of generalizing sensible approximations to the quantal energy levels.

At each of three frequencies ω/2π=26.43, 30.36, and 36.02 GHz, we observe 3d hydrogen atoms with certain principal quantum numbers ${\mathit{n}}_0$≫1 to be more stable against microwave ionization. Which ${\mathit{n}}_0$’s are more stable differs for each ω. Even when the enhanced stability is not found in 3d classical calculations, we show that it scales classically: This quantal effect occurs at certain values of the classically scaled frequency ${\mathit{n}}_0^3$ω. Our data give strong support for the enhanced stability being due to scarred 3d wave functions for the strongly driven atoms.

Mori theory leads to in(finite) continued fractions [I(F)CF’s] which upon inverse Laplace transformation (ILT) give the dynamical correlations in Hamiltonian systems. We propose a direct summation method to evaluate these ICF’s, e.g., 1/[z+${\mathrm{\Delta }}_1$/(z+... ∞)], by replacing them with FCF’s with poles L=${10}^{\mathrm{\zeta }}$, 2≤ζ≤5, for ${\mathrm{\Delta }}_{\mathrm{\mu }}$=${\mathrm{\mu }}^{\mathrm{\phi }}$, φ<2. Long-time dynamics is obtained upon an ILT of the ICF for 0≤t≤τ with τ=f(φ,ζ) being large. Our studies on dynamical correlations for boundary spins in S=1/2 XY chains agree very well with a recent exact solution for these correlations.

We study numerically by Padé approximants the analytic properties of the classical perturbation series parametrizing Kolmogorov-Arnold-Moser curves for the standard map. By complexifying the rotation number we show how the appearance of natural boundaries at diophantine real rotation numbers is a consequence of the accumulation of complex lines of singularities related to resonances. This provides a new intuitive understanding of the breakdown mechanism of invariant curves.

In conventional Einstein-Podolsky-Rosen (EPR) experiments an unstable system decays into an entangled state of two or more particles. When appropriate measurements are made on this entangled state, phenomena are exhibited that run counter to our classical notions of local realism. Using a variant of a gedanken experiment proposed by Greenberger, Horn, and Zeilinger, it is shown that EPR effects can arise even when the particles come from independent widely separated sources.

We discuss the spectra of quantized chaotic billiards from the point of view of scattering theory. We show that the spectral and the resonance density functions both fluctuate about a common mean. A semiclassical treatment explains this in terms of classical scattering trajectories and periodic orbits of the Poincaré scattering map. This formalism is used to interpret recent experiments where the spectra of chaotic cavities were measured by microwave scattering.

A multimode, autonomously chaotic solid-state laser system has been controlled by the technique of occassional proportional feedback, related to the control scheme of Ott, Grebogi, and Yorke. We show that complex periodic wave forms can be stabilized in the laser output intensity. A detailed model of the system is not necessary. Our results indicate that this control technique may be widely applicable to autonomous, higher-dimensional chaotic systems, including globally coupled arrays of nonlinear oscillators.

The tunneling in a double-well potential with dissipation is formulated without referring to instantons. This formulation, in the domain of small dissipation, goes beyond the instanton approximation. Several applications of this formulation for the Ohmic case are presented, and we show that the virtual mixing of excited states induced by dissipative interactions tends to enhance the tunneling rate. This enhancement effect becomes dominant for a super-Ohmic case.

A new stochastic method for the direct computation of real-time Green’s functions is proposed. The inherent sign problem is circumvented by partitioning the path integration into two parts, one of which involves conventional stochastic sampling, and the other explicit or analytical summation. Using this method, the dynamics of the spin-boson model may be computed up to several tunneling periods. The results reveal surprisingly complex relaxation behaviors near the coherent-incoherent boundary at low temperatures.

For a particular choice of vertex weights, the two-dimensional six-vertex model can be viewed as a probabilistic cellular automaton. Physically it describes then the surface slope of a two-dimensional solid which grows through deposition. Based on this analogy we predict the large-scale asymptotic behavior of the vertical polarization correlations. The transfer matrix commutes with a nonsymmetric spin Hamiltonian. We diagonalize it using the Bethe ansatz and prove that the dynamical scaling exponent for kinetic roughening is z=3/2 in 1+1 dimensions.

The probability distribution of the largest local Liapunov exponent is evaluated for a classical ${\mathrm{Ar}}_3$ cluster at different values of the internal energy E, for a set of increasing values of the length in which the trajectory is partitioned. These distributions can be directly related to the evolution of ergodic behavior, particularly to how it exhibits distinctive, separable time scales which depend strongly on the energy of the system. Therefore, even though the inequivalence of ergodicity and chaos prohibits a Liapunov exponent itself from being a quantitative index of ergodicity, we find that 2 the sample distributions used to evaluate Liapunov exponents nevertheless can be used for this purpose.

We have reexamined type-I intermittency, i.e., alternating bursts of regular and chaotic behavior just preceding a tangent bifurcation of the quadratic map family. By studying period-3 intermittency for the Hénon map family numerically, we establish the strong one-dimensional character of intermittency in the phase space. The disappearance of intermittency as the one-dimensional character of the map is lost (i.e., the dissipation is decreased) is reflected in a qualitative change in the behavior of the Lyapunov exponent in the period-1 basin of attraction.

Ekert has described a cryptographic scheme in which Einstein-Podolsky-Rosen (EPR) pairs of particles are used to generate identical random numbers in remote places, while Bell’s theorem certifies that the particles have not been measured in transit by an eavesdropper. We describe a related but simpler EPR scheme and, without invoking Bell’s theorem, prove it secure against more general attacks, including substitution of a fake EPR source. Finally we show our scheme is equivalent to the original 1984 key distribution scheme of Bennett and Brassard, which uses single particles instead of EPR pairs.