Microcanonical temperature for a classical field: Application to Bose-Einstein condensation

We show that the projected Gross-Pitaevskii equation (PGPE) can be mapped exactly onto Hamilton's equations of motion for classical position and momentum variables. Making use of this mapping, we adapt techniques developed in statistical mechanics to calculate the temperature and chemical potential of a classical Bose field in the microcanonical ensemble. We apply the method to simulations of the PGPE, which can be used to represent the highly occupied modes of Bose condensed gases at finite temperature. The method is rigorous, valid beyond the realms of perturbation theory, and agrees with an earlier method of temperature measurement for the same system. Using this method we show that the critical temperature for condensation in a homogeneous Bose gas on a lattice with a uv cutoff increases with the interaction strength. We discuss how to determine the temperature shift for the Bose gas in the continuum limit using this type of calculation, and obtain a result in agreement with more sophisticated Monte Carlo simulations. We also consider the behavior of the specific heat.

Coherent state construction of representations of osp(2|2) and primary fields of osp(2|2) conformal field theory

Representations of the superalgebra osp(2/2)(k)((1)) and current superalgebra. osp(2/2)k in the standard basis are investigated. All finite-dimensional typical and atypical representations of osp(2/2) are constructed by the vector coherent state method. Primary fields of the non-unitary conformal field theory associated with osp(2/2)(k)((1)) in the standard basis are obtained for arbitrary level k. (C) 2004 Elsevier B.V. All rights reserved.

Primary Fields and Screening Currents of gl (2/2) non-unitary conformal field theory

The non-semisimple gl(2)k current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible typical and atypical representations of gl(212) and three (two even and one odd) screening currents of the first kind are constructed explicitly in terms of ten free fields. (C) 2004 Elsevier B.V All rights reserved.

Evaluating the properties of a stage-specific self-efficacy scale for physical activity using classical test theory, confirmatory factor analysis and item response modeling

The purpose of this paper was to evaluate the psychometric properties of a stage-specific selfefficacy scale for physical activity with classical test theory (CTT), confirmatory factor analysis (CFA) and item response modeling (IRM). Women who enrolled in the Women On The Move study completed a 20-item stage-specific self-efficacy scale developed for this study [n = 226, 51.1% African-American and 48.9% Hispanic women, mean age = 49.2 (67.0) years, mean body mass index = 29.7 (66.4)]. Three analyses were conducted: (i) a CTT item analysis, (ii) a CFA to validate the factor structure and (iii) an IRM analysis. The CTT item analysis and the CFA results showed that the scale had high internal consistency (ranging from 0.76 to 0.93) and a strong factor structure. Results also showed that the scale could be improved by modifying or eliminating some of the existing items without significantly altering the content of the scale. The IRM results also showed that the scale had few items that targeted high self-efficacy and the stage-specific assumption underlying the scale was rejected. In addition, the IRM analyses found that the five-point response format functioned more like a four-point response format. Overall, employing multiple methods to assess the psychometric properties of the stage-specific self-efficacy scale demonstrated the complimentary nature of these methods and it highlighted the strengths and weaknesses of this scale.

Calculation of the microcanonical temperature for the classical Bose field

The ergodic hypothesis asserts that a classical mechanical system will in time visit every available configuration in phase space. Thus, for an ergodic system, an ensemble average of a thermodynamic quantity can equally well be calculated by a time average over a sufficiently long period of dynamical evolution. In this paper, we describe in detail how to calculate the temperature and chemical potential from the dynamics of a microcanonical classical field, using the particular example of the classical modes of a Bose-condensed gas. The accurate determination of these thermodynamics quantities is essential in measuring the shift of the critical temperature of a Bose gas due to nonperturbative many-body effects.

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.

Theory of strongly correlated electron systems. I. Intersite coulomb interaction and the approximation of renormalized fermions in total energy calculations

The diagrammatic strong-coupling perturbation theory (SCPT) for correlated electron systems is developed for intersite Coulomb interaction and for a nonorthogonal basis set. The construction is based on iterations of exact closed equations for many - electron Green functions (GFs) for Hubbard operators in terms of functional derivatives with respect to external sources. The graphs, which do not contain the contributions from the fluctuations of the local population numbers of the ion states, play a special role: a one-to-one correspondence is found between the subset of such graphs for the many - electron GFs and the complete set of Feynman graphs of weak-coupling perturbation theory (WCPT) for single-electron GFs. This fact is used for formulation of the approximation of renormalized Fermions (ARF) in which the many-electron quasi-particles behave analogously to normal Fermions. Then, by analyzing: (a) Sham's equation, which connects the self-energy and the exchange- correlation potential in density functional theory (DFT); and (b) the Galitskii and Migdal expressions for the total energy, written within WCPT and within ARF SCPT, a way we suggest a method to improve the description of the systems with correlated electrons within the local density approximation (LDA) to DFT. The formulation, in terms of renormalized Fermions LIDA (RF LDA), is obtained by introducing the spectral weights of the many electron GFs into the definitions of the charge density, the overlap matrices, effective mixing and hopping matrix elements, into existing electronic structure codes, whereas the weights themselves have to be found from an additional set of equations. Compared with LDA+U and self-interaction correction (SIC) methods, RF LDA has the advantage of taking into account the transfer of spectral weights, and, when formulated in terms of GFs, also allows for consideration of excitations and nonzero temperature. Going beyond the ARF SCPT, as well as RF LIDA, and taking into account the fluctuations of ion population numbers would require writing completely new codes for ab initio calculations. The application of RF LDA for ab initio band structure calculations for rare earth metals is presented in part 11 of this study (this issue). (c) 2005 Wiley Periodicals, Inc.

Properties of the stochastic Gross-Pitaevskii equation: finite temperature Ehrenfest relations and the optimal plane wave representation

We present Ehrenfest relations for the high temperature stochastic Gross-Pitaevskii equation description of a trapped Bose gas, including the effect of growth noise and the energy cutoff. A condition for neglecting the cutoff terms in the Ehrenfest relations is found which is more stringent than the usual validity condition of the truncated Wigner or classical field method-that all modes are highly occupied. The condition requires a small overlap of the nonlinear interaction term with the lowest energy single particle state of the noncondensate band, and gives a means to constrain dynamical artefacts arising from the energy cutoff in numerical simulations. We apply the formalism to two simple test problems: (i) simulation of the Kohn mode oscillation for a trapped Bose gas at zero temperature, and (ii) computing the equilibrium properties of a finite temperature Bose gas within the classical field method. The examples indicate ways to control the effects of the cutoff, and that there is an optimal choice of plane wave basis for a given cutoff energy. This basis gives the best reproduction of the single particle spectrum, the condensate fraction and the position and momentum densities.

Mean-field phase diagrams of imbalanced Fermi gases near a Feshbach resonance

We propose phase diagrams for an imbalanced (unequal number of atoms or Fermi surface in two pairing hyperfine states) gas of atomic fermions near a broad Feshbach resonance using mean-field theory. Particularly, in the plane of interaction and polarization we determine the region for a mixed phase composed of normal and superfluid components. We compare our prediction of phase boundaries with the recent measurement and find a good qualitative agreement.

Indications of coherence-incoherence crossover in layered metallic transport

For many strongly correlated metals with layered crystal structure the temperature dependence of the interlayer resistance is different to that of the intralayer resistance. We consider a small polaron model which exhibits this behavior, illustrating how the interlayer transport is related to the coherence of quasiparticles within the layers. Explicit results are also given for the electron spectral function, interlayer optical conductivity, and the interlayer magnetoresistance. All these quantities have two contributions: one coherent (dominant at low temperatures) and the other incoherent (dominant at high temperatures).

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.

Determination of protein charge by capillary zone electrophoresis

The feasibility of employing classical electrophoresis theory to determine the net charge (valence) of proteins by capillary zone electrophoresis is illustrated in this paper. An outline of a procedure to facilitate the interpretation of mobility measurements is demonstrated by its application to a published mobility measurement for Staphylococcal nuclease at pH 8.9 that had been obtained by capillary zone electrophoresis. The significantly higher valence of +7.5 (cf. 5.6 from the same series of measurements) that has been reported on the basis of a charge ladder approach for charge determination signifies the likelihood that the latter generic approach may be prone to error arising from nonconformity of the experimental system with an inherent assumption that chemical modification or mutation of amino acid residues has no effect on the overall three-dimensional size and shape of the protein. (C) 2004 Elsevier Inc. All rights reserved.

Multi-types of Skyrmions in SU(N) Quantum Hall System

The skyrmions in SU(N) quantum Hall (QH) system are discussed. By analyzing the gauge field structure and the topological properties of this QH system it is pointed out that in the SU(N) QH system there can exist (N-1) types of skyrmion structures, instead of only one type of skyrmions. In this paper, by means of the Abelian projections according to the (N-1) Cartan subalgebra local bases, we obtain the (N-1) U(1) electromagnetic field tensors in the SU(N) gauge field of the QH system, and then derive (N-1) types of skyrmion structures from these U(1) sub-field tensors. Furthermore, in light of the phi-mapping topological current method, the topological charges and the motion of these skyrmions are also discussed.