Quantum and classical chaos for a single trapped ion

In this paper we investigate the quantum and classical dynamics of a single trapped ion subject to nonlinear kicks derived from a periodic sequence of Gaussian laser pulses. We show that the classical system exhibits: diffusive growth in the energy, or heating,'' while quantum mechanics suppresses this heating. This system may be realized in current single trapped-ion experiments with the addition of near-field optics to introduce tightly focused laser pulses into the trap.

Neuromuscular-skeletal constraints upon the dynamics of unimanual and bimanual coordination

In the first of three experiments, 11 participants generated pronation and supination movements of the forearm, in time with an auditory metronome. The metronome frequency was increased in eight steps (0.25 Hz) from a base frequency of 1.75 Hz. On alternating trials, participants were required to coordinate either maximum pronation or maximum supination with each beat of the metronome. In each block of trials, the axis of rotation was either coincident with the long axis of the forearm, above this axis, or below this axis. The stability of the pronate-on-the-beat pattern, as indexed by the number of pattern changes, and the time of onset of pattern change, was greatest when the axis of rotation of the movement was below the long axis of the forearm. In contrast, the stability of the supinate-on-the-beat pattern was greatest when the axis of rotation of the movement was above the long axis of the forearm. In a second experiment, we examined how changes in the position of the axis of rotation alter the activation patterns of muscles that contribute to pronation and supination of the forearm. Variations in the relative dominance of the pronation and supination phases of the movement cycle across conditions were accounted for primarily by changes in the activation profile of flexor carpi radialis (FCR) and extensor carpi radialis longus (ECR). In the Final experiment we examined how these constraints impact upon the stability of bimanual coordination. Thirty-two participants were assigned at random to one of four conditions, each of which combined an axis of rotation configuration (bottom or top) for each limb. The participants generated both inphase (both limbs pronating simultaneously, and supinating simultaneously) and antiphase (left limb pronating and right limb supinating simultaneously, and vice versa) patterns of coordination. When the position of the axis of rotation was equivalent for the left and the right limb, transitions from antiphase to inphase patterns of coordination were Frequently observed. In marked contrast, when the position of the axis of rotation for the left and right limb was contradistinct, transitions From inphase to antiphase patterns of coordination occurred. The results demonstrated that when movements are performed in an appropriate mechanical context, inphase patterns of coordination are less stable than antiphase patterns.

Two-dimensional nonlinear dynamics of evanescent-wave guided atoms in a hollow fiber

We describe the classical and quantum two-dimensional nonlinear dynamics of large blue-detuned evanescent-wave guiding cold atoms in hollow fiber. We show that chaotic dynamics exists for classic dynamics, when the intensity of the beam is periodically modulated. The two-dimensional distributions of atoms in (x,y) plane are simulated. We show that the atoms will accumulate on several annular regions when the system enters a regime of global chaos. Our simulation shows that, when the atomic flux is very small, a similar distribution will be obtained if we detect the atomic distribution once each the modulation period and integrate the signals. For quantum dynamics, quantum collapses, and revivals appear. For periodically modulated optical potential, the variance of atomic position will be suppressed compared to the no modulation case. The atomic angular momentum will influence the evolution of wave function in two-dimensional quantum system of hollow fiber.

Multidimensional quantum solitons with nondegenerate parametric interactions: Photonic and Bose-Einstein condensate environments

We consider the quantum theory of three fields interacting via parametric and repulsive quartic couplings. This can be applied to treat photonic chi((2)) and chi((3)) interactions, and interactions in atomic Bose-Einstein condensates or quantum Fermi gases, describing coherent molecule formation together with a-wave scattering. The simplest two-particle quantum solitons or bound-state solutions of the idealized Hamiltonian, without a momentum cutoff, are obtained exactly. They have a pointlike structure in two and three dimensions-even though the corresponding classical theory is nonsingular. We show that the solutions can be regularized with a momentum cutoff. The parametric quantum solitons have much more realistic length scales and binding energies than chi((3)) quantum solitons, and the resulting effects could potentially be experimentally tested in highly nonlinear optical parametric media or interacting matter-wave systems. N-particle quantum solitons and the ground state energy are analyzed using a variational approach. Applications to atomic/molecular Bose-Einstein condensates (BEC's) are given, where we predict the possibility of forming coupled BEC solitons in three space dimensions, and analyze superchemistry dynamics.

Computational chemistry on Fujitsu vector-parallel processors: Development and performance of applications software

In this and a preceding paper, we provide an introduction to the Fujitsu VPP range of vector-parallel supercomputers and to some of the computational chemistry software available for the VPP. Here, we consider the implementation and performance of seven popular chemistry application packages. The codes discussed range from classical molecular dynamics to semiempirical and ab initio quantum chemistry. All have evolved from sequential codes, and have typically been parallelised using a replicated data approach. As such they are well suited to the large-memory/fast-processor architecture of the VPP. For one code, CASTEP, a distributed-memory data-driven parallelisation scheme is presented. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

Nitrogen dynamics and the physiological basis of stay-green in sorghum

Sorghum [Sorghum bicolor (L,) Moench] hybrids containing the stay-green trait retain more photosynthetically active leaves under drought than do hybrids that do not contain this trait. Since the Longevity and photosynthetic capacity of a leaf are related to its N status, it is important to clarify the role of N in extending leaf greenness in stay-green hybrids. Field studies were conducted in northeastern Australia to examine the effect of three water regimes and nine hybrids on N uptake and partitioning among organs. Nine hybrids varying in the B35 and KS19 sources of stay-green were grown under a fully irrigated control, post-flowering water deficit, and terminal water deficit. For hybrids grown under terminal water deficit, stay-green was viewed as a consequence of the balance between N demand by the grain and N supply during gain filling. On the demand side, grain numbers were 16% higher in the four stay-green than in the five senescent hybrids. On the supply side, age-related senescence provided an average of 34 and 42 kg N ha(-1) for stay-green and senescent hybrids, respectively. In addition, N uptake during grain filling averaged 116 and 82 kg ha(-1) in stay-green and senescent hybrids. Matching the N supply from these two sources with grain N demand found that the shortfall in N supply for grain filling in the stay-green and senescent hybrids averaged 32 and 41 kg N ha(-1) resulting in more accelerated leaf senescence in the senescent hybrids. Genotypic differences in delayed onset and reduced rate of leaf senescence were explained by differences in specific leaf nitrogen and N uptake during grain filling. Leaf nitrogen concentration at anthesis was correlated with onset (r = 0.751**, n = 27) and rate (r = -0.783**, n = 27) of leaf senescence ender terminal water deficit.

Sensitivity to measurement perturbation of single-atom dynamics in cavity QED

We consider continuous observation of the nonlinear dynamics of single atom trapped in an optical cavity by a standing wave with intensity modulation. The motion of the atom changes the phase of the field which is then monitored by homodyne detection of the output field. We show that the conditional Hilbert space dynamics of this system, subject to measurement-induced perturbations, depends strongly on whether the corresponding classical dynamics is regular or chaotic. If the classical dynamics is chaotic, the distribution of conditional Hilbert space vectors corresponding to different observation records tends to be orthogonal. This is a characteristic feature of hypersensitivity to perturbation for quantum chaotic systems.

Atoms in an amplitude-modulated standing wave - dynamics and pathways to quantum chaos

Cold rubidium atoms are subjected to an amplitude-modulated far-detuned standing wave of light to form a quantum-driven pendulum. Here we discuss the dynamics of these atoms. Phase space resonances and chaotic transients of the system exhibit dynamics which can be useful in many atom optics applications as they can be utilized as means for phase space state preparation. We explain the occurrence of distinct peaks in the atomic momentum distribution, analyse them in detail and give evidence for the importance of the system for quantum chaos and decoherence studies.

Determination of activation energy distributions for chemisorption of oxygen on carbon: an improved approach

The present paper proposes an approach to obtaining the activation energy distribution for chemisorption of oxygen onto carbon surfaces, while simultaneously allowing for the activation energy dependence of the pre-exponential factor of the rate constant. Prior studies in this area have considered this factor to be uniform, thereby biasing estimated distributions. The results show that the derived activation energy distribution is not sensitive to the chemisorption mechanism because of the step function like property of the coverage. The activation energy distribution is essentially uniform for some carbons, and has two or possibly more discrete stages, suggestive of at least two types of sites, each with its own uniform distribution. The pre-exponential factors of the reactions are determined directly from the experimental data, and are found not to be constant as assumed in earlier work, but correlated with the activation energy. The latter results empirically follow an exponential function, supporting some earlier statistical and experimental work. The activation energy distribution obtained in the present paper permits improved correlation of chemisorption data in comparison to earlier studies. (C) 2000 Elsevier Science Ltd. All rights reserved.

Quantum chaos in atom optics

I shall discuss the quantum and classical dynamics of a class of nonlinear Hamiltonian systems. The discussion will be restricted to systems with one degree of freedom. Such systems cannot exhibit chaos, unless the Hamiltonians are time dependent. Thus we shall consider systems with a potential function that has a higher than quadratic dependence on the position and, furthermore, we shall allow the potential function to be a periodic function of time. This is the simplest class of Hamiltonian system that can exhibit chaotic dynamics. I shall show how such systems can be realized in atom optics, where very cord atoms interact with optical dipole potentials of a far-off resonance laser. Such systems are ideal for quantum chaos studies as (i) the energy of the atom is small and action scales are of the order of Planck's constant, (ii) the systems are almost perfectly isolated from the decohering effects of the environment and (iii) optical methods enable exquisite time dependent control of the mechanical potentials seen by the atoms.

Context-free and context-sensitive dynamics in recurrent neural networks

Continuous-valued recurrent neural networks can learn mechanisms for processing context-free languages. The dynamics of such networks is usually based on damped oscillation around fixed points in state space and requires that the dynamical components are arranged in certain ways. It is shown that qualitatively similar dynamics with similar constraints hold for a(n)b(n)c(n), a context-sensitive language. The additional difficulty with a(n)b(n)c(n), compared with the context-free language a(n)b(n), consists of 'counting up' and 'counting down' letters simultaneously. The network solution is to oscillate in two principal dimensions, one for counting up and one for counting down. This study focuses on the dynamics employed by the sequential cascaded network, in contrast to the simple recurrent network, and the use of backpropagation through time. Found solutions generalize well beyond training data, however, learning is not reliable. The contribution of this study lies in demonstrating how the dynamics in recurrent neural networks that process context-free languages can also be employed in processing some context-sensitive languages (traditionally thought of as requiring additional computation resources). This continuity of mechanism between language classes contributes to our understanding of neural networks in modelling language learning and processing.

Accelerating seismic energy release and evolution of event time and size statistics: Results from two heterogeneous cellular automaton models

The evolution of event time and size statistics in two heterogeneous cellular automaton models of earthquake behavior are studied and compared to the evolution of these quantities during observed periods of accelerating seismic energy release Drier to large earthquakes. The two automata have different nearest neighbor laws, one of which produces self-organized critical (SOC) behavior (PSD model) and the other which produces quasi-periodic large events (crack model). In the PSD model periods of accelerating energy release before large events are rare. In the crack model, many large events are preceded by periods of accelerating energy release. When compared to randomized event catalogs, accelerating energy release before large events occurs more often than random in the crack model but less often than random in the PSD model; it is easier to tell the crack and PSD model results apart from each other than to tell either model apart from a random catalog. The evolution of event sizes during the accelerating energy release sequences in all models is compared to that of observed sequences. The accelerating energy release sequences in the crack model consist of an increase in the rate of events of all sizes, consistent with observations from a small number of natural cases, however inconsistent with a larger number of cases in which there is an increase in the rate of only moderate-sized events. On average, no increase in the rate of events of any size is seen before large events in the PSD model.

Energy and averages in the mechanics of granular materials

We derive a general thermo-mechanical theory for particulate materials consisting of granules of arbitrary whose material points possess three translational and three independent rotational degrees of freedom. Additional field variables are the translational and rotational granular temperatures, the kinetic energies shape and size. The kinematics of granulate is described within the framework of a polar continuum theory of the velocity and spin fluctuations respectively and the usual thermodynamic temperature. We distinguish between averages over particle categories (averages in mass/velocity and moment of inertia/spin space, respectively) and particle phases where the average extends over distinct subsets of particle categories (multi phase flows). The relationship between the thermal energy in the granular system and phonon energy in a molecular system is briefly discussed in the main body of the paper and discussed in detail in the Appendix A. (C) 2001 Elsevier Science B.V. All rights reserved.

Dynamics of trapped Bose-Einstein condensates: Beyond the mean-field

Since dilute Bose gas condensates were first experimentally produced, the Gross-Pitaevskii equation has been successfully used as a descriptive tool. As a mean-field equation, it cannot by definition predict anything about the many-body quantum statistics of condensate. We show here that there are a class of dynamical systems where it cannot even make successful predictions about the mean-field behavior, starting with the process of evaporative cooling by which condensates are formed. Among others are parametric processes, such as photoassociation and dissociation of atomic and molecular condensates.

Prediction of carbon monoxide in fires by conditional moment closure

Carbon monoxide is the chief killer in fires. Dangerous levels of CO can occur when reacting combustion gases are quenched by heat transfer, or by mixing of the fire plume in a cooled under- or overventilated upper layer. In this paper, carbon monoxide predictions for enclosure fires are modeled by the conditional moment closure (CMC) method and are compared with laboratory data. The modeled fire situation is a buoyant, turbulent, diffusion flame burning under a hood. The fire plume entrains fresh air, and the postflame gases are cooled considerably under the hood by conduction and radiation, emulating conditions which occur in enclosure fires and lead to the freezing of CO burnout. Predictions of CO in the cooled layer are presented in the context of a complete computational fluid dynamics solution of velocity, temperature, and major species concentrations. A range of underhood equivalence ratios, from rich to lean, are investigated. The CMC method predicts CO in very good agreement with data. In particular, CMC is able to correctly predict CO concentrations in lean cooled gases, showing its capability in conditions where reaction rates change considerably.