Integrable Models: from Dynamical Solutions to String Theory

We review the status of integrable models from the point of view of their dynamics and integrability conditions. A few integrable models are discussed in detail. We comment on the use it is made of them in string theory. We also discuss the SO(6) symmetric Hamiltonian with SO(6) boundary. This work is especially prepared for the 70th anniversaries of Andr, Swieca (in memoriam) and Roland Koberle.

Generalized non-commutative inflation

Non-commutative geometry indicates a deformation of the energy-momentum dispersion relation f (E) = E/pc (not equal 1) for massless particles. This distorted energy-momentum relation can affect the radiation-dominated phase of the universe at sufficiently high temperature. This prompted the idea of non-commutative inflation by Alexander et al (2003 Phys. Rev. D 67 081301) and Koh and Brandenberger (2007 JCAP06(2007) 021 and JCAP11(2007) 013). These authors studied a one-parameter family of a non-relativistic dispersion relation that leads to inflation: the a family of curves f (E) = 1 + (lambda E)(alpha). We show here how the conceptually different structure of symmetries of non-commutative spaces can lead, in a mathematically consistent way, to the fundamental equations of non-commutative inflation driven by radiation. We describe how this structure can be considered independently of (but including) the idea of non-commutative spaces as a starting point of the general inflationary deformation of SL(2, C). We analyze the conditions on the dispersion relation that leads to inflation as a set of inequalities which plays the same role as the slow-roll conditions on the potential of a scalar field. We study conditions for a possible numerical approach to obtain a general one-parameter family of dispersion relations that lead to successful inflation.

Coupled Boltzmann calculation of mixed axion/neutralino cold dark matter production in the early universe

We calculate the relic abundance of mixed axion/neutralino cold dark matter which arises in R-parity conserving supersymmetric (SUSY) models wherein the strong CP problem is solved by the Peccei-Quinn (PQ) mechanism with a concommitant axion/saxion/axino supermultiplet. By numerically solving the coupled Boltzmann equations, we include the combined effects of 1. thermal axino production with cascade decays to a neutralino LSP, 2. thermal saxion production and production via coherent oscillations along with cascade decays and entropy injection, 3. thermal neutralino production and re-annihilation after both axino and saxion decays, 4. gravitino production and decay and 5. axion production both thermally and via oscillations. For SUSY models with too high a standard neutralino thermal abundance, we find the combined effect of SUSY PQ particles is not enough to lower the neutralino abundance down to its measured value, while at the same time respecting bounds on late-decaying neutral particles from BBN. However, models with a standard neutralino underabundance can now be allowed with either neutralino or axion domination of dark matter, and furthermore, these models can allow the PQ breaking scale f(a) to be pushed up into the 10(14) - 10(15) GeV range, which is where it is typically expected to be in string theory models.

Multibrane solutions in cubic superstring field theory

Using the elements of the so-called KBc gamma subalgebra, we study a class of analytic solutions depending on a single function F(K) in the modified cubic superstring field theory. We compute the energy associated to these solutions and show that the result can be expressed in terms of a contour integral. For a particular choice of the function F(K), we show that the energy is given by integer multiples of a single D-brane tension.

Stochastic gravito-inertial modes discovered by CoRoT in the hot Be star HD51452

Context. Be stars are rapidly rotating stars with a circumstellar decretion disk. They usually undergo pressure and/or gravity pulsation modes excited by the kappa-mechanism, i.e. an effect of the opacity of iron-peak elements in the envelope of the star. In the Milky Way, p-modes are observed in stars that are hotter than or equal to the B3 spectral type, while g-modes are observed at the B2 spectral type and cooler. Aims. We observed a B0IVe star, HD51452, with the high-precision, high-cadence photometric CoRoT satellite and high-resolution, ground-based HARPS and SOPHIE spectrographs to study its pulsations in great detail. We also used the lower resolution spectra available in the BeSS database. Methods. We analyzed the CoRoT and spectroscopic data with several methods: CLEAN-NG, FREQFIND, and a sliding window method. We also analyzed spectral quantities, such as the violet over red (V/R) emission variations, to obtain information about the variation in the circumstellar environment. We calculated a stellar structure model with the ESTER code to test the various interpretation of the results. Results. We detect 189 frequencies of variations in the CoRoT light curve in the range between 0 and 4.5 c d(-1). The main frequencies are also recovered in the spectroscopic data. In particular we find that HD51452 undergoes gravito-inertial modes that are not in the domain of those excited by the kappa-mechanism. We propose that these are stochastic modes excited in the convective zones and that at least some of them are a multiplet of r-modes (i.e. subinertial modes mainly driven by the Coriolis acceleration). Stochastically excited gravito-inertial modes had never been observed in any star, and theory predicted that their very low amplitudes would be undetectable even with CoRoT. We suggest that the amplitudes are enhanced in HD51452 because of the very rapid stellar rotation. In addition, we find that the amplitude variations of these modes are related to the occurrence of minor outbursts. Conclusions. Thanks to CoRoT data, we have detected a new kind of pulsations in HD51452, which are stochastically excited gravito-inertial modes, probably due to its very rapid rotation. These modes are probably also present in other rapidly rotating hot Be stars.

Conceptual problem for noncommutative inflation and the new approach for nonrelativistic inflationary equation of state

In a previous paper, we connected the phenomenological noncommutative inflation of Alexander, Brandenberger and Magueijo [ Phys. Rev. D 67 081301 (2003)] and Koh and Brandenberger [ J. Cosmol. Astropart Phys. 2007 21 ()] with the formal representation theory of groups and algebras and analyzed minimal conditions that the deformed dispersion relation should satisfy in order to lead to a successful inflation. In that paper, we showed that elementary tools of algebra allow a group-like procedure in which even Hopf algebras (roughly the symmetries of noncommutative spaces) could lead to the equation of state of inflationary radiation. Nevertheless, in this paper, we show that there exists a conceptual problem with the kind of representation that leads to the fundamental equations of the model. The problem comes from an incompatibility between one of the minimal conditions for successful inflation (the momentum of individual photons being bounded from above) and the Fock-space structure of the representation which leads to the fundamental inflationary equations of state. We show that the Fock structure, although mathematically allowed, would lead to problems with the overall consistency of physics, like leading to a problematic scattering theory, for example. We suggest replacing the Fock space by one of two possible structures that we propose. One of them relates to the general theory of Hopf algebras (here explained at an elementary level) while the other is based on a representation theorem of von Neumann algebras (a generalization of the Clebsch-Gordan coefficients), a proposal already suggested by us to take into account interactions in the inflationary equation of state.

Stochastic gravito-inertial modes discovered by CoRoT in the hot Be star HD51452

Context. Be stars are rapidly rotating stars with a circumstellar decretion disk. They usually undergo pressure and/or gravity pulsation modes excited by the κ-mechanism, i.e. an effect of the opacity of iron-peak elements in the envelope of the star. In the Milky Way, p-modes are observed in stars that are hotter than or equal to the B3 spectral type, while g-modes are observed at the B2 spectral type and cooler. Aims. We observed a B0IVe star, HD51452, with the high-precision, high-cadence photometric CoRoT satellite and high-resolution, ground-based HARPS and SOPHIE spectrographs to study its pulsations in great detail. We also used the lower resolution spectra available in the BeSS database. Methods. We analyzed the CoRoT and spectroscopic data with several methods: Clean-NG, FreqFind, and a sliding window method. We also analyzed spectral quantities, such as the violet over red (V/R) emission variations, to obtain information about the variation in the circumstellar environment. We calculated a stellar structure model with the ESTER code to test the various interpretation of the results. Results. We detect 189 frequencies of variations in the CoRoT light curve in the range between 0 and 4.5 c d−1. The main frequencies are also recovered in the spectroscopic data. In particular we find that HD51452 undergoes gravito-inertial modes that are not in the domain of those excited by the κ-mechanism. We propose that these are stochastic modes excited in the convective zones and that at least some of them are a multiplet of r-modes (i.e. subinertial modes mainly driven by the Coriolis acceleration). Stochastically excited gravito-inertial modes had never been observed in any star, and theory predicted that their very low amplitudes would be undetectable even with CoRoT. We suggest that the amplitudes are enhanced in HD51452 because of the very rapid stellar rotation. In addition, we find that the amplitude variations of these modes are related to the occurrence of minor outbursts. Conclusions. Thanks to CoRoT data, we have detected a new kind of pulsations in HD51452, which are stochastically excited gravito-inertial modes, probably due to its very rapid rotation. These modes are probably also present in other rapidly rotating hot Be stars.

Study of the Influence of Localized Vibrational Modes in Charge Transport Properties at Nanoscale Systems.

In molecular and atomic devices the interaction between electrons and ionic vibrations has an important role in electronic transport. The electron-phonon coupling can cause the loss of the electron's phase coherence, the opening of new conductance channels and the suppression of purely elastic ones. From the technological viewpoint phonons might restrict the efficiency of electronic devices by energy dissipation, causing heating, power loss and instability. The state of the art in electron transport calculations consists in combining ab initio calculations via Density Functional Theory (DFT) with Non-Equilibrium Green's Function formalism (NEGF). In order to include electron-phonon interactions, one needs in principle to include a self-energy scattering term in the open system Hamiltonian which takes into account the effect of the phonons over the electrons and vice versa. Nevertheless this term could be obtained approximately by perturbative methods. In the First Born Approximation one considers only the first order terms of the electronic Green's function expansion. In the Self-Consistent Born Approximation, the interaction self-energy is calculated with the perturbed electronic Green's function in a self-consistent way. In this work we describe how to incorporate the electron-phonon interaction to the SMEAGOL program (Spin and Molecular Electronics in Atomically Generated Orbital Landscapes), an ab initio code for electronic transport based on the combination of DFT + NEGF. This provides a tool for calculating the transport properties of materials' specific system, particularly in molecular electronics. Preliminary results will be presented, showing the effects produced by considering the electron-phonon interaction in nanoscale devices.

From inflation to dark energy through a dynamical Λ: an attempt at alleviating fundamental cosmic puzzles

After decades of successful hot big-bang paradigm, cosmology still lacks a framework in which the early inflationary phase of the universe smoothly matches the radiation epoch and evolves to the present “quasi” de Sitter spacetime. No less intriguing is that the current value of the effective vacuum energy density is vastly smaller than the value that triggered inflation. In this paper, we propose a new class of cosmologies capable of overcoming, or highly alleviating, some of these acute cosmic puzzles. Powered by a decaying vacuum energy density, the spacetime emerges from a pure nonsingular de Sitter vacuum stage, “gracefully” exits from inflation to a radiation phase followed by dark matter and vacuum regimes, and, finally, evolves to a late-time de Sitter phase.