Generalized Boltzmann equation for a trapped Bose-condensed gas using the Kadanoff-Baym formalism

Using the Kadanoff-Baym non-equilibrium Green's function formalism, we derive kinetic equations for the non-condensate atoms at finite temperatures which include the effect of binary collisions between atoms. The effect of collisions is included using the second-order self-energy given by the Beliaev (gapless) approximation. We limit our discussion to finite temperatures where we can use the single-particle Hartree-Fock spectrum for the excited atoms. In this limit, we can neglect the off-diagonal propagators ($\tilde{g}_{12}$ and $\tilde{g}_{21}$). As expected, this leads to the kinetic equations and collision integrals used in recent work by Zaremba, Nikuni, and Griffin (ZNG) [1]. We also derive a consistent equation of motion for the condensate wavefunction, involving a finite-temperature generalization of the well-known Gross-Pitaevskii equation which includes a dissipative term, as well as the mean field of the non-condensate.Comment: Given at the workshop on ``Kadanoff-Baym Equations'', Rostock, Sept. 20-24, 1999. To be published in the proceedings by World Scientifi

The Beliaev Broken Symmetry Description of Superfluidity vs the Classical-Field Approach

The standard theoretical basis for understanding superfluidity in Bose systems was formulated by Beliaev in 1957, based on splitting the quantum field operator into a macroscopically occupied condensate component and a non-condensate component. This leads to a description of the condensate in terms of a 'single-particle state', the so-called macroscopic wavefunction. Since the discovery of Bose-condensed gases, an alternative theoretical picture has been developed which is based on a 'coherent band' of classically occupied states. This is often called the classical or c-field approach. The goal of this chapter is to review the differences between the Beliaev broken symmetry and c-field approach, and to argue that the c-field concept of a coherent condensate band of states has problems as a description of Bose superfluidity. However, the c-field idea of treating the lowest energy excitations classically can be used to advantage to simplify calculations within the Beliaev broken-symmetry formalism.Comment: 6 pages. Unedited version of chapter to appear in Quantum Gases: Finite Temperature and Non-Equilibrium Dynamics (Vol. 1 Cold Atoms Series). N.P. Proukakis, S.A. Gardiner, M.J. Davis and M.H. Szymanska, eds. Imperial College Press, London (in press). See http://www.icpress.co.uk/physics/p817.html v2: Added arXiv cross-reference

Landau damping of Bogoliubov excitations in optical lattices at finite temperature

We study the damping of Bogoliubov excitations in an optical lattice at finite temperatures. For simplicity, we consider a Bose-Hubbard tight-binding model and limit our analysis to the lowest excitation band. We use the Popov approximation to calculate the temperature dependence of the number of condensate atoms $n^{\rm c 0}(T)$ in each lattice well. We calculate the Landau damping of a Bogoliubov excitation in an optical lattice due to coupling to a thermal cloud of excitations. While most of the paper concentrates on 1D optical lattices, we also briefly present results for 2D and 3D lattices. For energy conservation to be satisfied, we find that the excitations in the collision process must exhibit anomalous dispersion ({\it i.e.} the excitation energy must bend upward at low momentum), as also exhibited by phonons in superfluid $^4\rm{He}$. This leads to the sudden disappearance of all damping processes in $D$-dimensional simple cubic optical lattice when $U n^{\rm c 0}\ge 6DJ$, where $U$ is the on-site interaction, and $J$ is the hopping matrix element. Beliaev damping in a 1D optical lattice is briefly discussed.Comment: 28 pages, 9 figure

Stratigraphy and Structure of Central Maine

Guidebook for field trips in east-central and north-central Maine: 66th annual meeting October 12 and 13, 1974: Trip B-

Damping of Bogoliubov Excitations in Optical Lattices

Extending recent work to finite temperatures, we calculate the Landau damping of a Bogoliubov excitation in an optical lattice, due to coupling to a thermal cloud of such excitations. For simplicity, we consider a 1D Bose-Hubbard model and restrict ourselves to the first energy band. For energy conservation to be satisfied, the excitations in the collision processes must exhibit ``anomalous dispersion'', analogous to phonons in superfluid $^4\rm{He}$. This leads to the disappearance of all damping processes when $U n^{\rm c 0}\ge 6t$, where $U$ is the on-site interaction, $t$ is the hopping matrix element and $n^{\rm c 0}(T)$ is the number of condensate atoms at a lattice site. This phenomenon also occurs in 2D and 3D optical lattices. The disappearance of Beliaev damping above a threshold wavevector is noted.Comment: 4pages, 5figures, submitted to Phys. Rev. Let

Методологические аспекты понятия инновационности в современных условиях развития постиндустриального производства

В статье анализируются особенности постиндустриального производства, особенности современного развития социально-экономических систем, обосновывается необходимость поиска более совершенных подходов к процессу управления развитием, анализируется необходимость изучения особенности инновационности как элемента понятийного аппарата системы инновационного развития с точки зрения материалистической диалектики современной волновой теории развития и значение в этом процессе новообразования.The article analyzes the peculiarities of post-industrial production, the features of modern development of socio-economic systems, the necessity for a claim of more sophisticated approaches to the process of development management, analyzes the necessity of studying the characteristics of innovation as an element of the conceptual apparatus of the system of innovative development from the point of view of the materialist dialectic of modern wave theory of development and the importance in this process neoplasm

Shiny Apps: The Evolution of Extension Tools from Spreadsheets to New Interactive Dashboards

The Interactive web dashboard is the newness with characteristics and features that are replacing the status quo downloading spreadsheets. RStudio is the program used to create Shiny Apps dashboards with R. We explain some of those features so that Extension specialists can adopt the methodology, engage stakeholders, and help them understand and apply results to their production systems, although we do not explain the creation process step by step. Our approach offers not only a useful and modern way to disseminate information to empower decision-making, but also a safe environment in which data can be automatically updated and users cannot inadvertently corrupt the tool