Critical fluctuations and entanglement in the nondegenerate parametric oscillator

We present a fully quantum mechanical treatment of the nondegenerate optical parametric oscillator both below and near threshold. This is a nonequilibrium quantum system with a critical point phase transition, that is also known to exhibit strong yet easily observed squeezing and quantum entanglement. Our treatment makes use of the positive P representation and goes beyond the usual linearized theory. We compare our analytical results with numerical simulations and find excellent agreement. We also carry out a detailed comparison of our results with those obtained from stochastic electrodynamics, a theory obtained by truncating the equation of motion for the Wigner function, with a view to locating regions of agreement and disagreement between the two. We calculate commonly used measures of quantum behavior including entanglement, squeezing, and Einstein-Podolsky-Rosen (EPR) correlations as well as higher order tripartite correlations, and show how these are modified as the critical point is approached. These results are compared with those obtained using two degenerate parametric oscillators, and we find that in the near-critical region the nondegenerate oscillator has stronger EPR correlations. In general, the critical fluctuations represent an ultimate limit to the possible entanglement that can be achieved in a nondegenerate parametric oscillator.

Critical Temperature of a Trapped Bose Gas: Comparison of Theory and Experiment

We apply the projected Gross-Pitaevskii equation (PGPE) formalism to the experimental problem of the shift in critical temperature T-c of a harmonically confined Bose gas as reported in Gerbier , Phys. Rev. Lett. 92, 030405 (2004). The PGPE method includes critical fluctuations and we find the results differ from various mean-field theories, and are in best agreement with experimental data. To unequivocally observe beyond mean-field effects, however, the experimental precision must either improve by an order of magnitude, or consider more strongly interacting systems. This is the first application of a classical field method to make quantitative comparison with experiment.

Quantum criticality

We investigate the theory of quantum fluctuations in non-equilibrium systems having large critical fluctuations. This allows us to treat the limits imposed by nonlinearities to quantum squeezing and noise reduction, and also to envisage future tests of quantum theory in regions of macroscopic quantum fluctuations. A long-term objective of this research is to identify suitable physical systems in which macroscopic 'Schrodinger cat'-like behaviour may be observed. We investigate two systems in particular of much current experimental interest, namely the degenerate parametric oscillator near threshold, and the evaporatively cooled (BEC). We compare the results obtained in the positive-P representation, as a fully quantum mechanical calculation, with the truncated Wigner phase space equation, also known as semi-classical theory. We show when these results agree and differ in calculations taken beyond the linearized approximation. In the region where the largest quantum fluctuations and Schrodinger cat-like behaviour might be expected, we find that the quantum predictions correspond very closely to the semi-classical theory. Nature abhors observing a Schrodinger car.

Haptic information stabilizes and destabilizes coordination dynamics

Goal-directed, coordinated movements in humans emerge from a variety of constraints that range from 'high-level' cognitive strategies based oil perception of the task to 'low-level' neuromuscular-skeletal factors such as differential contributions to coordination from flexor and extensor muscles. There has been a tendency in the literature to dichotomize these sources of constraint, favouring one or the other rather than recognizing and understanding their mutual interplay. In this experiment, subjects were required to coordinate rhythmic flexion and extension movements with an auditory metronome, the rate of which was systematically increased. When subjects started in extension on the beat of the metronome, there was a small tendency to switch to flexion at higher rates, but not vice versa. When subjects: were asked to contact a physical stop, the location of which was either coincident with or counterphase to the auditor) stimulus, two effects occurred. When haptic contact was coincident with sound, coordination was stabilized for both flexion and extension. When haptic contact was counterphase to the metronome, coordination was actually destabilized, with transitions occurring from both extension to flexion on the beat and from flexion to extension on the beat. These results reveal the complementary nature of strategic and neuromuscular factors in sensorimotor coordination. They also suggest the presence of a multimodal neural integration process-which is parametrizable by rate and context - in which intentional movement, touch and sound are bound into a single, coherent unit.

Effector dynamics of rhythmic wrist activity and its implications for (modeling) bimanual coordination

To examine the role of the effector dynamics of the wrist in the production of rhythmic motor activity, we estimated the phase shifts between the EMG and the task-related output for a rhythmic isometric torque production task and an oscillatory movement, and found a substantial difference (45-52degrees) between the two. For both tasks, the relation between EMG and task-related output (torque or displacement) was adequately reproduced with a physiologically motivated musculoskeletal model. The model simulations demonstrated the importance of the contribution of passive structures to the overall dynamics and provided an account for the observed phase shifts in the dynamic task. Additional simulations of the musculoskeletal model with added load suggested that particular changes in the phase relation between EMG and movement may follow largely from the intrinsic muscle dynamics, rather than being the result of adaptations in the neural control of joint stiffness. The implications of these results are discussed in relation to (models of) interlimb coordination in rhythmic tasks. (C) 2004 Elsevier B.V. All rights reserved.

Critical quantum fluctuations in the degenerate parametric oscillator

We develop a systematic theory of critical quantum fluctuations in the driven parametric oscillator. Our analytic results agree well with stochastic numerical simulations. We also compare the results obtained in the positive-P representation, as a fully quantum-mechanical calculation, with the truncated Wigner phase-space equation, also known as the semiclassical theory. We show when these results agree and differ in calculations taken beyond the linearized approximation. We find that the optimal broadband noise reduction occurs just above threshold. In this region where there are large quantum fluctuations in the conjugate variance and macroscopic quantum superposition states might be expected, we find that the quantum predictions correspond very closely to the semiclassical theory.

Charged hadron multiplicity fluctuations in Au+Au and Cu+Cu collisions from root S(NN) = 22.5 to 200 GeV

A comprehensive survey of event-by-event fluctuations of charged hadron multiplicity in relativistic heavy ions is presented. The survey covers Au+Au collisions at s(NN)=62.4 and 200 GeV, and Cu+Cu collisions at s(NN)=22.5,62.4, and 200 GeV. Fluctuations are measured as a function of collision centrality, transverse momentum range, and charge sign. After correcting for nondynamical fluctuations due to fluctuations in the collision geometry within a centrality bin, the remaining dynamical fluctuations expressed as the variance normalized by the mean tend to decrease with increasing centrality. The dynamical fluctuations are consistent with or below the expectation from a superposition of participant nucleon-nucleon collisions based upon p+p data, indicating that this dataset does not exhibit evidence of critical behavior in terms of the compressibility of the system. A comparison of the data with a model where hadrons are independently emitted from a number of hadron clusters suggests that the mean number of hadrons per cluster is small in heavy ion collisions.

On the relationship between the critical temperature and the London penetration depth in layered organic superconductors

We present an analysis of previously published measurements of the London penetration depth of layered organic superconductors. The predictions of the BCS theory of superconductivity are shown to disagree with the measured zero temperature, in plane, London penetration depth by up to two orders of magnitude. We find that fluctuations in the phase of the superconducting order parameter do not determine the superconducting critical temperature as the critical temperature predicted for a Kosterlitz–Thouless transition is more than an order of magnitude greater than is found experimentally for some materials. This places constraints on theories of superconductivity in these materials.

Patchy populations in stochastic environments: Critical number of patches for persistence

We introduce a model for the dynamics of a patchy population in a stochastic environment and derive a criterion for its persistence. This criterion is based on the geometric mean (GM) through time of the spatial-arithmetic mean of growth rates. For the population to persist, the GM has to be greater than or equal to1. The GM increases with the number of patches (because the sampling error is reduced) and decreases with both the variance and the spatial covariance of growth rates. We derive analytical expressions for the minimum number of patches (and the maximum harvesting rate) required for the persistence of the population. As the magnitude of environmental fluctuations increases, the number of patches required for persistence increases, and the fraction of individuals that can be harvested decreases. The novelty of our approach is that we focus on Malthusian local population dynamics with high dispersal and strong environmental variability from year to year. Unlike previous models of patchy populations that assume an infinite number of patches, we focus specifically on the effect that the number of patches has on population persistence. Our work is therefore directly relevant to patchily distributed organisms that are restricted to a small number of habitat patches.

Light receptor action is critical for maintaining plant biomass at warm ambient temperatures.

The ability to withstand environmental temperature variation is essential for plant survival. Former studies in Arabidopsis revealed that light signalling pathways had a potentially unique role in shielding plant growth and development from seasonal and daily fluctuations in temperature. In this paper we describe the molecular circuitry through which the light receptors cry1 and phyB buffer the impact of warm ambient temperatures. We show that the light signalling component HFR1 acts to minimise the potentially devastating effects of elevated temperature on plant physiology. Light is known to stabilise levels of HFR1 protein by suppressing proteasome-mediated destruction of HFR1. We demonstrate that light-dependent accumulation and activity of HFR1 are highly temperature dependent. The increased potency of HFR1 at warmer temperatures provides an important restraint on PIF4 that drives elongation growth. We show that warm ambient temperatures promote the accumulation of phosphorylated PIF4. However, repression of PIF4 activity by phyB and cry1 (via HFR1) is critical for controlling growth and maintaining physiology as temperatures rise. Loss of this light-mediated restraint has severe consequences for adult plants which have greatly reduced biomass.

Critical ruptures in a bundle of slowly relaxing fibers

We study the damage enhanced creep rupture of disordered materials by means of a fiber bundle model. Broken fibers undergo a slow stress relaxation modeled by a Maxwell element whose stress exponent m can vary in a broad range. Under global load sharing we show that due to the strength disorder of fibers, the lifetime ʧ of the bundle has sample-to-sample fluctuations characterized by a log-normal distribution independent of the type of disorder. We determine the Monkman-Grant relation of the model and establish a relation between the rupture life tʄ and the characteristic time tm of the intermediate creep regime of the bundle where the minimum strain rate is reached, making possible reliable estimates of ʧ from short term measurements. Approaching macroscopic failure, the deformation rate has a finite time power law singularity whose exponent is a decreasing function of m. On the microlevel the distribution of waiting times is found to have a power law behavior with m-dependent exponents different below and above the critical load of the bundle. Approaching the critical load from above, the cutoff value of the distributions has a power law divergence whose exponent coincides with the stress exponent of Maxwell elements

Quantum critical effects in mean-field glassy systems

We consider the effects of quantum fluctuations in mean-field quantum spin-glass models with pairwise interactions. We examine the nature of the quantum glass transition at zero temperature in a transverse field. In models (such as the random orthogonal model) where the classical phase transition is discontinuous an analysis using the static approximation reveals that the transition becomes continuous at zero temperature.

Distribution and role of macrophytes in coastal lagoons : implications of critical shifts

Crossroads, crucibles and refuges are three words that may describe natural coastal lagoon environments. The words refer to the complex mix of marine and terrestrial influences, prolonged dilution due to the semi-enclosed nature and the function of a habitat for highly diverse plant and animal communities, some of which are endangered. To attain a realistic picture of the present situation, high vulnerability to anthropogenic impact should be added to the description. As the sea floor in coastal lagoons is usually entirely photic, macrophyte primary production is accentuated compared with open sea environments. There is, however, a lack of proper knowledge on the importance of vegetation for the general functioning of coastal lagoon ecosystems. The aim of this thesis is to assess the role of macrophyte diversity, cover and species identity over temporal and spatial scales for lagoon functions, and to determine which steering factors primarily restrict the qualitative and quantitative composition of vegetation in coastal lagoons. The results are linked to patterns of related trophic levels and the indicative potential of vegetation for assessment of general conditions in coastal lagoons is evaluated. This thesis includes five field studies conducted in flads and glo-flads in the brackish water northern Baltic Sea. Flads and glo-flads are defined as a Baltic variety of coastal lagoons, which due to an inlet threshold and post-glacial landuplift slowly will be isolated from the open sea. This process shrinks inlet size, increases exposure and water retention, and is called habitat isolation. The studied coastal lagoons are situated in the archipelago areas of the eastern coast of Sweden, the Åland Islands and the south-west mainland of Finland, where land-uplift amounts to ca. 5 mm/ per year. Out of 400 evaluated sites, a total of 70 lagoons varying in inlet size, archipelago position and anthropogenic influence to cover for essential environmental variation were chosen for further inventory. Vegetation composition, cover and richness were measured together with several hydrographic and morphometric variables in the lagoons both seasonally and inter-annually to cover for general regional, local and temporal patterns influencing lagoon and vegetation development. On smaller species-level scale, the effects of macrophyte species identity and richness for the fish habitat function were studied by examining the influence of plant interaction on juvenile fish diversity. Thus, the active election of plant monoand polycultures by fish and the diversity of fish in the respective culture were examined and related to plant height and water depth. The lagoons and vegetation composition were found to experience a regime shift initiated by increased habitat isolation along with land-uplift. Vegetation composition altered, richness decreased and cover increased forming a less isolated and more isolated regime, named the vascular plant regime and charophyte regime, respectively according to the dominant vegetation. As total phosphorus in the water, turbidity and the impact of regional influences decreased in parallel, the dominance of charophytes and increasing cover seemed to buffer and stabilize conditions in the charophyte regime and indicated an increased functional role of vegetation for the lagoon ecosystem. The regime pattern was unaffected by geographical differences, while strong anthropogenic impact seemed to distort the pattern due to loss of especially Chara tomentosa L. in the charophyte regime. The regimes were further found unperturbed by short-time temporal fluctuations. In fact the seasonal and inter-annual dynamics reinforced the functional difference between the regimes by the increasing role of vegetation along habitat isolation and the resemblance to lake environments for the charophyte regime. For instance, greater total phosphorus and chlorophyll a concentrations in the water in the beginning of the season in the charophyte regime compared with the vascular plant regime presented a steeper reduction to even lower values than in the vascular plant regime along the season. Despite a regional importance and positive relationship of macrophyte diversity in relation to trophic diversity, species identity was underlined in the results of this thesis, especially with decreasing spatial scale. This result was supported partly by the increased role of charophytes in the functioning of the charophyte regime, but even more explicitly by the species-specific preference of juvenile fish for tall macrophyte monocultures. On a smaller species-level scale, tall plant species in monoculture seemed to be able to increase their length, indicating that negative selection forms preferred habitat structures, which increase fish diversity. This negative relationship between plant and fish diversity suggest a shift in diversity patterns among trohic levels on smaller scale. Thus, as diversity patterns seem complex and diverge among spatial scales, it might be ambiguous to extend the understanding of diversity relationships from one trophic level to the other. All together, the regime shift described here presents similarities to the regime development in marine lagoon environments and shallow lakes subjected to nutrient enrichment. However, due to nutrient buffering by vegetation with increased isolation and water retention as a consequence of the inlet threshold, the development seems opposite to the course along an eutrophication gradient described in marine lagoons lacking an inlet threshold, where the role of vegetation decreases. Thus, the results imply devastating consequences of inlet dredging (decreasing isolation) in terms of vegetation loss and nutrient release, and call for increased conservational supervision. Especially the red listed charophytes would suffer negatively from such interference and the consequences are likely to also deteriorate juvenile fish production. The fact that a new species to Finland, Chara connivens Salzm. Ex. Braun 1835 was discovered during this study further indicates a potential of the lagoons serving as refuges for rare species.

Quantum critical effects in mean-field glassy systems

We consider the effects of quantum fluctuations in mean-field quantum spin-glass models with pairwise interactions. We examine the nature of the quantum glass transition at zero temperature in a transverse field. In models (such as the random orthogonal model) where the classical phase transition is discontinuous an analysis using the static approximation reveals that the transition becomes continuous at zero temperature.

CRITICAL BEHAVIOR AND THRESHOLD OF COEXISTENCE OF A PREDATOR-PREY STOCHASTIC MODEL IN A 2D LATTICE

We investigate the critical behavior of a stochastic lattice model describing a predator-prey system. By means of Monte Carlo procedure we simulate the model defined on a regular square lattice and determine the threshold of species coexistence, that is, the critical phase boundaries related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. A finite size scaling analysis is employed to determine the order parameter, order parameter fluctuations, correlation length and the critical exponents. Our numerical results for the critical exponents agree with those of the directed percolation universality class. We also check the validity of the hyperscaling relation and present the data collapse curves.