We study the formation of a Bose-Einstein condensate in a cigar-shaped three-dimensional harmonic trap, induced by the controlled addition of an attractive "dimple" potential along the weak axis. In this manner we are able to induce condensation without cooling due to a localized increase in the phase-space density. We perform a quantitative analysis of the thermodynamic transformation in both the sudden and adiabatic regimes for a range of dimple widths and depths. We find good agreement with equilibrium calculations based on self-consistent semiclassical Hartree-Fock theory describing the condensate and thermal cloud. We observe that there is an optimal dimple depth that results in a maximum in the condensate fraction. We also study the nonequilibrium dynamics of condensate formation in the sudden turn-on regime, finding good agreement for the observed time dependence of the condensate fraction with calculations based on quantum kinetic theory.

Abstract. In this paper we present an efficient model of the neuronal potentials recorded by a deep brain stimulation microelectrode (DBS MER) in the subthalamic nucleus. It is shown that a computationally efficient filtered point process consisting of 10,000 neurons, including extracellular filtering closely matches recordings from 14 Parkinson's disease patients. The recordings were compared using their voltage amplitude distributions, power spectral density estimates and phase synchrony. It was found that interspike interval times modeled using a Weibull distribution with a shape parameter of 0.8, slightly non-Poisosnian, gave the best fit of the simulations to patient recordings. These results indicate that part of the 'background activity' present in an DBS MER can be considered to be a very local field potential due to the surrounding neuronal activity.Therefore, the statistics of the interspike interval times modify the structure of the background activity.

A theoretical investigation into the behaviour of the Non-Markov Parameter is performed from a signal processing perspective in contrast to previous methodologies based on stochastic processes theory. The results indicate that the NMP can be regarded as an informational metric which is indicative of the degree of low frequency synchronisation in a complex system. These results have deep implications for physiological analysis of biological systems where the presence of sychronisation is often a marker of pathological functioning. The NMP measure is then applied to in vivo micro-electrode recordings from the subthalamic nucleus.

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