Dynamic correlation functions in one-dimensional quasi-condensates

We calculate the static and dynamic single-particle correlation functions in one-dimensional (1D) trapped Bose gases and discuss experimental measurements that can directly probe such correlation functions. Using a quantized hydrodynamic theory for the low energy excitations, we calculate both the static and dynamic single-particle correlation functions for a 1D Bose gas that is a phase-fluctuating quasi-condensate. For the static (equal-time) correlation function, our approximations and results are equivalent to those of Petrov, Shlyapnikov and Walraven. The Fourier transform of the static single-particle correlation function gives the momentum distribution, which can be measured using Doppler-sensitive Bragg scattering experiments on a highly elongated Bose gas. We show how a two-photon Raman out-coupling experiment can measure the characteristic features of the dynamic or time-dependent single-particle correlation function of a 1D Bose quasi-condensate.Comment: 19 pages, 4 figures; submitted to Phys. Rev.

Finite-temperature correlations in the one-dimensional trapped and untrapped Bose gases

We calculate the dynamic single-particle and many-particle correlation functions at non-zero temperature in one-dimensional trapped repulsive Bose gases. The decay for increasing distance between the points of these correlation functions is governed by a scaling exponent that has a universal expression in terms of observed quantities. This expression is valid in the weak-interaction Gross-Pitaevskii as well as in the strong-interaction Girardeau-Tonks limit, but the observed quantities involved depend on the interaction strength. The confining trap introduces a weak center-of-mass dependence in the scaling exponent. We also conjecture results for the density-density correlation function.Comment: 18 pages, Latex, Revtex

Bosonizing one-dimensional cold atomic gases

We present results for the long-distance asymptotics of correlation functions of mesoscopic one-dimensional systems with periodic and open (Dirichlet) boundary conditions, as well as at finite temperature in the thermodynamic limit. The results are obtained using Haldane's harmonic-fluid approach (also known as ``bosonization''), and are valid for both bosons and fermions, in weakly and strongly interacting regimes. The harmonic-fluid approach and the method to compute the correlation functions using conformal transformations are explained in great detail. As an application relevant to one-dimensional systems of cold atomic gases, we consider the model of bosons interacting with a zero-range potential. The Luttinger-liquid parameters are obtained from the exact solution by solving the Bethe-ansatz equations in finite-size systems. The range of applicability of the approach is discussed, and the prefactor of the one-body density matrix of bosons is fixed by finding an appropriate parametrization of the weak-coupling result. The formula thus obtained is shown to be accurate, when compared with recent diffusion Montecarlo calculations, within less than 10%. The experimental implications of these results for Bragg scattering experiments at low and high momenta are also discussed.Comment: 39 pages + 14 EPS figures; typos corrected, references update

Momentum distribution and correlation function of quasicondensates in elongated traps

We calculate the spatial correlation function and momentum distribution of a phase-fluctuating, elongated three-dimensional condensate, in a trap and in free expansion. We take the inhomogeneous density profile into account {\it{via}} a local density approximation. We find an almost Lorentzian momentum distribution, in stark contrast with a Heisenberg-limited Thomas-Fermi condensate.Comment: 5 pages, 2 figures; final version, references update

Investigation of an optimalising controller

Includes bibliography.This dissertation presents a comprehensive investigation of an optimalising controller and its behaviour when controlling a simulated plant. In addition certain theoretical aspects of optimalising control are presented. Design criteria and details of the circuitry of the experimental controller, built as part of this research project, are given. The necessity to deactivate the controller, for a certain period during each cycle of operation, is shown to be a result of measurement delay in the optimalising loop, and an expression for evaluating the deactive time is derived. Utilising describing function techniques, the steady-state response of the control system is predicted and the results are shown to be in good agreement with the experimental results. The adaptive response of the system is investigated and it is shown that the bandwidth of the adaptive response maybe predicted from steady-state response characteristics. The limitations imposed upon both the steady-state and adaptive response, by measurement delay, are shown . With respect to the theory of optimalising control, a framework for stability analysis is developed and stability criteria for the basic optimalising control loop are derived

The Dilution Dependency of Multigroup Uncertainties

The propagation of nuclear data uncertainties through reactor physics calculation has received attention through the Organization for Economic Cooperation and Development—Nuclear Energy Agency’s Uncertainty Analysis in Modelling (UAM) benchmark. A common strategy for performing lattice physics uncertainty analysis involves starting with nuclear data and covariance matrix which is typically available at infinite dilution. To describe the uncertainty of all multigroup physics parameters—including those at finite dilution—additional calculations must be performed that relate uncertainties in an infinite dilution cross-section to those at the problem dilution. Two potential methods for propagating dilution-related uncertainties were studied in this work. The first assumed a correlation between continuous-energy and multigroup cross-sectional data and uncertainties, which is convenient for direct implementation in lattice physics codes. The second is based on a more rigorous approach involving the Monte Carlo sampling of resonance parameters in evaluated nuclear data using the TALYS software. When applied to a light water fuel cell, the two approaches show significant differences, indicating that the assumption of the first method did not capture the complexity of physics parameter data uncertainties. It was found that the covariance of problem-dilution multigroup parameters for selected neutron cross-sections can vary significantly from their infinite-dilution counterparts