132 research outputs found
Exponential localization of Wannier functions in insulators
No full textThe exponential localization of Wannier functions in two or three dimensions is proven for all insulators that display time-reversal symmetry, settling a long-standing conjecture. Our proof relies on the equivalence between the existence of analytic quasi-Bloch functions and the nullity of the Chern numbers (or of the Hall current) for the system under consideration. The same equivalence implies that Chern insulators cannot display exponentially localized Wannier functions. An explicit condition for the reality of the Wannier functions is identified
Quantum field theory meets Hopf algebra
No full text27 pages, 4 figures. Slightly edited version of the published paperInternational audienceThis paper provides a primer in quantum field theory (QFT) based on Hopf algebra and describes new Hopf algebraic constructions inspired by QFT concepts. The following QFT concepts are introduced: chronological products, S-matrix, Feynman diagrams, connected diagrams, Green functions, renormalization. The use of Hopf algebra for their definition allows for simple recursive derivations and lead to a correspondence between Feynman diagrams and semi-standard Young tableaux. Reciprocally, these concepts are used as models to derive Hopf algebraic constructions such as a connected coregular action or a group structure on the linear maps from S(V) to V. In most cases, noncommutative analogues are derived
A differential identity for Green functions
No full text14 pagesInternational audienceIf P is a differential operator with constant coefficients, an identity is derived to calculate the action of exp(P) on the product of two functions. In many-body theory, P describes the interaction Hamiltonian and the identity yields a hierarchy of Green functions. The identity is first derived for scalar fields and the standard hierarchy is recovered. Then the case of fermions is considered and the identity is used to calculate the generating function for the Green functions of an electron system in a time-dependent external potential
Consultative Committee for Space Data Systems
No full textThe major space agencies of the world recognize that there are benefits in using standard techniques for handling space data and that, by cooperatively developing these techniques, future data system interoperability will be enhanced. In order to assure that work towards standardization of space-related information technologies provides the maximum benefi t for
the interested agencies, both individually and collectively, an international Consultative Committee for Space Data Systems (CCSDS) was established in 1982 as a forum for international cooperation in the development of data handling techniques supporting space research, including space science and
applications. In 1991, the committee was incorporated as a subcommittee of the International Organization for Standardization (ISO).
The article describs the work of CCSDS till its beginning in the 80s till today (2009)
Analytical solutions for two-level systems with damping
No full text4 pagesInternational audienceA method is proposed to transform any analytic solution of the Bloch equation into an analytic solution of the Landau-Lifshitz-Gilbert equation. This allows for the analytical description of the dynamics of a two level system with damping. This method shows that damping turns the linear Schrödinger equation of a two-level system into a nonlinear Schrödinger equation. As applications, it is shown that damping has a relatively mild influence on self-induced transparency but destroys dynamical localization
Lie Group Calculation of the Green Function of Disordered Systems
No full textABSTRACTWithin the framework of the muffin-tin multiple-scattering theory, the scattering path operators are given by the inverse of a matrix consisting of atomic t-matrices and a structural matrix. The influence of the displacement of an atomic centre on the structural matrix can be described analytically using Lie group techniques. From this analytical expression and the standard perturbation expansion of the Lippmann-Schwinger equation, it is possible to write the Green function of a disordered system as a series of terms whichare averages over configurations. These averages can be calculated analytically from themoments of the interatomic distances. Special terms of this series are then summed up toinfinity using Dyson equation. This formalism is computationally very effective to calculate electronic properties of systems with thermal or structural disorder. In this paper, the theoretical basis of this approach is briefly described and the convergence properties of the expansions are investigated.</jats:p
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