Classical and quantum dynamics of a model for atomic-molecular Bose-Einstein condensates

We study a model for a two-mode atomic-molecular Bose-Einstein condensate. Starting with a classical analysis we determine the phase space fixed points of the system. It is found that bifurcations of the fixed points naturally separate the coupling parameter space into four regions. The different regions give rise to qualitatively different dynamics. We then show that this classification holds true for the quantum dynamics.

Experimental tests of quantum nonlinear dynamics in atom optics

Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose-Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck's constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 out of phase with the initial state.

The Paradoxes of Paramountcy: Regional Rivalries and the Dynamics of American Hegemony in East Asia

It has become increasingly commonplace to describe the United States as hegemonic. And yet, despite America's dominant position at a number of levels strategic, political-economic and ideational, there are plainly limits to US hegemony. These limits and the enduring strengths of American hegemony are revealed quite clearly in East Asia. This paper critically assesses a number of theories of hegemony, and argues that the concept continues to provide a useful way of conceptualising America's evolving relationship with East Asia. Theories of hegemony can, with appropriate caveats, also help us to understand the limits to Chinese and Japanese power in the region; two countries that are routinely cited as potential hegemonic rivals

Exact solution, scaling behaviour and quantum dynamics of a model of an atom-molecule Bose-Einstein condensate

0We study the exact solution for a two-mode model describing coherent coupling between atomic and molecular Bose-Einstein condensates (BEC), in the context of the Bethe ansatz. By combining an asymptotic and numerical analysis, we identify the scaling behaviour of the model and determine the zero temperature expectation value for the coherence and average atomic occupation. The threshold coupling for production of the molecular BEC is identified as the point at which the energy gap is minimum. Our numerical results indicate a parity effect for the energy gap between ground and first excited state depending on whether the total atomic number is odd or even. The numerical calculations for the quantum dynamics reveals a smooth transition from the atomic to the molecular BEC.

Fock-state dynamics in Raman photoassociation of Bose-Einstein condensates

By stochastic modeling of the process of Raman photoassociation of Bose-Einstein condensates, we show that, the farther the initial quantum state is from a coherent state, the farther the one-dimensional predictions are from those of the commonly used zero-dimensional approach. We compare the dynamics of condensates, initially in different quantum states, finding that, even when the quantum prediction for an initial coherent state is relatively close to the Gross-Pitaevskii prediction, an initial Fock state gives qualitatively different predictions. We also show that this difference is not present in a single-mode type of model, but that the quantum statistics assume a more important role as the dimensionality of the model is increased. This contrasting behavior in different dimensions, well known with critical phenomena in statistical mechanics, makes itself plainly visible here in a mesoscopic system and is a strong demonstration of the need to consider physically realistic models of interacting condensates.

Modelling, nitrogen dynamics in sugarcane systems: Recent advances and applications

Substantial amounts of nitrogen (N) fertiliser are necessary for commercial sugarcane production because of the large biomass produced by sugarcane crops. Since this fertiliser is a substantial input cost and has implications if N is lost to the environment, there are pressing needs to optimise the supply of N to the crops' requirements. The complexity of the N cycle and the strong influence of climate, through its moderation of N transformation processes in the soil and its impact on N uptake by crops, make simulation-based approaches to this N management problem attractive. In this paper we describe the processes to be captured in modelling soil and plant N dynamics in sugarcane systems, and review the capability for modelling these processes. We then illustrate insights gained into improved management of N through simulation-based studies for the issues of crop residue management, irrigation management and greenhouse gas emissions. We conclude by identifying processes not currently represented in the models used for simulating N cycling in sugarcane production systems, and illustrate ways in which these can be partially overcome in the short term. (c) 2005 Elsevier B.V. All rights reserved.

Analysis of articulatory dynamics in dysarthria following brain injury in childhood using electromagnetic articulography and electropalatography

Two physiological assessments, electromagnetic articulography (EMA) and electropalatography (EPG), were used simultaneously to investigate the articulatory dynamics in an 18-year-old male with dysarthria 9 years following traumatic brain injury (TBI). Eight words consisting of /t, s, integral, k/ in word initial and word final positions were produced up to 10 times. A nonneurologically impaired male served as a control subject. Six parameters were analyzed using EMA: velocity, acceleration, deceleration, distance, duration, and motion path of tongue movements. Using EPG, the pattern and amount of tongue-to-palate contact and the duration of the closure/constriction phase of each consonant produced were assessed. Timing disturbances in the TBI speaker's speech were highlighted in perceptual assessments in the form of prolonged phonemes and a reduced speech rate. EMA analysis revealed that the approach and release phase durations of the consonant productions were within normal limits. Kinematic strategies such as decreased velocity and decreased distances traveled by the tongue, however, may have counterbalanced each other to produce these appropriate results. EPG examination revealed significantly longer closure/constriction phase periods, which may have contributed to the prolonged phonemes and reduced speech rate observed. The implications of these findings for the development of treatment programs for dysarthria subsequent to TBI will be highlighted.