Non-equilibrium dynamics of a Bose-Einstein condensate in an optical lattice

The dynamical evolution of a Bose-Einstein condensate trapped in a one-dimensional lattice potential is investigated theoretically in the framework of the Bose-Hubbard model. The emphasis is set on the far-from-equilibrium evolution in a case where the gas is strongly interacting. This is realized by an appropriate choice of the parameters in the Hamiltonian, and by starting with an initial state, where one lattice well contains a Bose-Einstein condensate while all other wells are empty. Oscillations of the condensate as well as non-condensate fractions of the gas between the different sites of the lattice are found to be damped as a consequence of the collisional interactions between the atoms. Functional integral techniques involving self-consistently determined mean fields as well as two-point correlation functions are used to derive the two-particle-irreducible (2PI) effective action. The action is expanded in inverse powers of the number of field components N, and the dynamic equations are derived from it to next-to-leading order in this expansion. This approach reaches considerably beyond the Hartree-Fock-Bogoliubov mean-field theory, and its results are compared to the exact quantum dynamics obtained by A.M. Rey et al., Phys. Rev. A 69, 033610 (2004) for small atom numbers.Comment: 9 pages RevTeX, 3 figure

Ward Identities for the 2PI effective action in QED

We study the issue of symmetries and associated Ward-like identities in the context of two-particle-irreducible (2PI) functional techniques for abelian gauge theories. In the 2PI framework, the $n$-point proper vertices of the theory can be obtained in various different ways which, although equivalent in the exact theory, differ in general at finite approximation order. We derive generalized (2PI) Ward identities for these various $n$-point functions and show that such identities are exactly satisfied at any approximation order in 2PI QED. In particular, we show that 2PI-resummed vertex functions, i.e. field-derivatives of the so-called 2PI-resummed effective action, exactly satisfy standard Ward identities. We identify another set of $n$-point functions in the 2PI framework which exactly satisfy the standard Ward identities at any approximation order. These are obtained as field-derivatives of the two-point function \bcG^{-1}[\phi], which defines the extremum of the 2PI effective action. We point out that the latter is not constrained by the underlying symmetry. As a consequence, the well-known fact that the corresponding gauge-field polarization tensor is not transverse in momentum space for generic approximations does not constitute a violation of (2PI) Ward identities. More generally, our analysis demonstrates that approximation schemes based on 2PI functional techniques respect all the Ward identities associated with the underlying abelian gauge symmetry. Our results apply to arbitrary linearly realized global symmetries as well.Comment: 33 pages, 2 figure

2PI Effective Action and Evolution Equations of N = 4 super Yang-Mills

We employ nPI effective action techniques to study N = 4 super Yang-Mills, and write down the 2PI effective action of the theory. We also supply the evolution equations of two-point correlators within the theory.Comment: 16 pages, 6 figures. Figure 2 replaced, approximation scheme clarified, references adde

Simultaneous analysis of natural pigments and E-141i in olive oils by liquid chromatography-tandem mass spectrometry

This work describes the development of an ultra-high-performance liquid chromatography-tandem mass spectrometry (UHPLC-MS/MS) method for the determination of carotenoids (β-carotene, lutein, β-criptoxanthin, neoxanthin, violaxanthin) and chlorophylls, as well as their related compounds (chlorophyll A and B, pheophytin A and B and the banned dyes Cu-pyropheophytin A, Cu-pheophytin A and B) in olive oils. For this purpose, the feasibility of electrospray ionization (ESI), atmospheric pressure chemical ionization (APCI) and atmospheric pressure photoionization (APPI) for the ionization of these compounds was evaluated and compared. Tandem mass spectrometry (MS/MS) fragmentation was discussed for each family of compounds, and the most characteristic and abundant product ions were selected to propose a selective and sensitive UHPLC-MS/MS method. The best results were obtained using APCI and APPI, while ESI provided the worst signal-to-noise ratio (S/N) for all compounds. For the analysis of olive oils, a simple solid-phase extraction (SPE) with silica cartridges was applied before the determination by UHPLC-MS/MS (APCI and APPI) in multiple reaction monitoring (MRM) mode. Method quality parameters were stablished, and the results demonstrate the good performance of the new methods, providing low limits of detection (0.004-0.9 mg L−1), high extraction efficiencies (62-95%) and low matrix effects (< 25%). The developed UHPLC-API-MS/MS(APCI and APPI) methods were applied to the analysis of olive oil samples, and β-carotene, pheophytinA, pheophytin B and lutein were detected and quantified in all of them at concentrations ranging from 0.1 to 9.5 mg L−1

Age-length keys availability for Atlantic bluefin tuna captured in the eastern management area

This paper analyzes the available direct ageing information in the last decade from Atlantic bluefin tuna caught in the eastern management area. To investigate differences among ALKs, a standard Von Bertalanffy growth function (VB) was fit to length at age data for each stratum. A deficient convergence of VB fitting to the asymptotic length due to the scarcity of old specimens was found for all available ALKs. After these analyses some records were identified as outliers (reading methodological issues) and removed from the data base.En prensa0,000

Quantum versus classical statistical dynamics of an ultracold Bose gas

We investigate the conditions under which quantum fluctuations are relevant for the quantitative interpretation of experiments with ultracold Bose gases. This requires to go beyond the description in terms of the Gross-Pitaevskii and Hartree-Fock-Bogoliubov mean-field theories, which can be obtained as classical (statistical) field-theory approximations of the quantum many-body problem. We employ functional-integral techniques based on the two-particle irreducible (2PI) effective action. The role of quantum fluctuations is studied within the nonperturbative 2PI 1/N expansion to next-to-leading order. At this accuracy level memory-integrals enter the dynamic equations, which differ for quantum and classical statistical descriptions. This can be used to obtain a 'classicality' condition for the many-body dynamics. We exemplify this condition by studying the nonequilibrium evolution of a 1D Bose gas of sodium atoms, and discuss some distinctive properties of quantum versus classical statistical dynamics.Comment: 19 pages, 10 figure