Interaction of strongly correlated electrons and acoustical phonons

We investigate the interaction of correlated electrons with acoustical phonons using the extended Hubbard-Holstein model in which both, the electron-phonon interaction and the on-site Coulomb repulsion are considered to be strong. The Lang-Firsov canonical transformation allows to obtain mobile polarons for which a new diagram technique and generalized Wick's theorem is used. This allows to handle the Coulomb repulsion between the electrons emerged into a sea of phonon fields (\textit{phonon clouds}). The physics of emission and absorption of the collective phonon-field mode by the polarons is discussed in detail. Moreover, we have investigated the different behavior of optical and acoustical phonon clouds when propagating through the lattice. In the strong-coupling limit of the electron-phonon interaction, and in the normal as well as in the superconducting phase, chronological thermodynamical averages of products of acoustical phonon-cloud operators can be expressed by one-cloud operator averages. While the normal one-cloud propagator has the form of a Lorentzian, the anomalous one is of Gaussian form and considerably smaller. Therefore, the anomalous electron Green's functions can be considered to be more important than corresponding polarons functions, i.e., pairing of electrons without phonon-clouds is easier to achieve than pairing of polarons with such clouds.Comment: : 28 pages, 9 figures, revtex4. Invited paper for a special issue of Low Temperature Physics dedicated to the 20th anniversary of HTS

Constraints on cosmic-ray propagation models from a global Bayesian analysis

Research in many areas of modern physics such as, e.g., indirect searches for dark matter and particle acceleration in SNR shocks, rely heavily on studies of cosmic rays (CRs) and associated diffuse emissions (radio, microwave, X-rays, gamma rays). While very detailed numerical models of CR propagation exist, a quantitative statistical analysis of such models has been so far hampered by the large computational effort that those models require. Although statistical analyses have been carried out before using semi-analytical models (where the computation is much faster), the evaluation of the results obtained from such models is difficult, as they necessarily suffer from many simplifying assumptions, The main objective of this paper is to present a working method for a full Bayesian parameter estimation for a numerical CR propagation model. For this study, we use the GALPROP code, the most advanced of its kind, that uses astrophysical information, nuclear and particle data as input to self-consistently predict CRs, gamma rays, synchrotron and other observables. We demonstrate that a full Bayesian analysis is possible using nested sampling and Markov Chain Monte Carlo methods (implemented in the SuperBayeS code) despite the heavy computational demands of a numerical propagation code. The best-fit values of parameters found in this analysis are in agreement with previous, significantly simpler, studies also based on GALPROP.Comment: 19 figures, 3 tables, emulateapj.sty. A typo is fixed. To be published in the Astrophysical Journal v.728 (February 10, 2011 issue). Supplementary material can be found at http://www.g-vo.org/pub/GALPROP/GalpropBayesPaper

Diagrammatic theory for Periodic Anderson Model: Stationary property of the thermodynamic potential

Diagrammatic theory for Periodic Anderson Model has been developed, supposing the Coulomb repulsion of $f-$ localized electrons as a main parameter of the theory. $f-$ electrons are strongly correlated and $c-$ conduction electrons are uncorrelated. Correlation function for $f-$ and mass operator for $c-$ electrons are determined. The Dyson equation for $c-$ and Dyson-type equation for $f-$ electrons are formulated for their propagators. The skeleton diagrams are defined for correlation function and thermodynamic functional. The stationary property of renormalized thermodynamic potential about the variation of the mass operator is established. The result is appropriate as for normal and as for superconducting state of the system.Comment: 12 pages, 10 figure

What can GLAST say about the origin of cosmic rays in other galaxies ?

Gamma rays in the band from 20 MeV to 300 GeV, used in combination with data from radio and X-ray bands, provide a powerful tool for studying the origin of cosmic rays in our sister galaxies Andromeda and the Magellanic Clouds. Gamma-ray Large Area Space Telescope (GLAST) will spatially resolve these galaxies and measure the spectrum and intensity of diffuse gamma radiation from the collisions of cosmic rays with gas and dust in them. Observations of Andromeda will give an external perspective on a spiral galaxy like the Milky Way. Observations of the Magellanic Clouds will permit a study of cosmic rays in dwarf irregular galaxies, where the confinement is certainly different and the massive star formation rate is much greater.Comment: 4 pages including 6 figures; to appear in Proc. ACE-2000 Symp. "The Acceleration and Transport of Energetic Particles Observed in the Heliosphere" (Jan. 5-8, 2000, Indian Wells, CA), AIP Conf. Proc. More details can be found at the LHEA GLAST page at http://lhea-glast.gsfc.nasa.gov/pub/science/index.htm

Spin solitons in magnetized pair plasmas

A set of fluid equations, taking into account the spin properties of the electrons and positrons in a magnetoplasma, are derived. The magnetohydrodynamic limit of the pair plasma is investigated. It is shown that the microscopic spin properties of the electrons and positrons can lead to interesting macroscopic and collective effects in strongly magnetized plasmas. In particular, it is found that new Alfvenic solitary structures, governed by a modified Korteweg-de Vries equation, are allowed in such plasmas. These solitary structures vanish if the quantum spin effects are neglected. Our results should be of relevance for astrophysical plasmas, e.g. in pulsar magnetospheres.Comment: 7 page

Strong interaction of correlated electrons with phonons: Exchange of phonon clouds by polarons

We investigate the interaction of strongly correlated electrons with phonons in the frame of the Hubbard-Holstein model. The electron-phonon interaction is considered to be strong and is an important parameter of the model besides the Coulomb repulsion of electrons and band filling. This interaction with the nondispersive optical phonons has been transformed to the problem of mobile polarons by using the canonical transformation of Lang and Firsov. We discuss in particular the case for which the on-site Coulomb repulsion is exactly cancelled by the phonon-mediated attractive interaction and suggest that polarons exchanging phonon clouds can lead to polaron pairing and superconductivity. It is then the frequency of the collective mode of phonon clouds being larger than the bare frequency, which determines the superconducting transition temperature.Comment: 23 pages, Submitted to Phys. Rev.

Diagrammatic analysis of the Hubbard model:Stationary property of the thermodynamic potential

Diagrammatic approach proposed many years ago for strong correlated Hubbard model is developed for analyzing of the thermodynamic potential properties. The new exact relation between such renormalized quantities as thermodynamic potential, one-particle propagator and correlation function is established. This relation contains additional integration of the one-particle propagator by the auxiliary constant. The vacuum skeleton diagrams constructed from irreducible Green's functions and tunneling propagator lines are determined and special functional is introduced. The properties of such functional are investigated and its relation to the thermodynamic potential is established. The stationary properties of this functional with respect to first order changing of the correlation function is demonstrated and as a consequence the stationary properties of the thermodynamic potential is proved.Comment: 6 pages, 4 figure

The Phosphorus, Sulfur, Argon, and Calcium Isotopic Composition of the Galactic Cosmic Ray Source

Galactic cosmic ray (GCR) measurements of the phosphorus, sulfur, argon, and calcium isotopes made by the Cosmic Ray Isotope Spectrometer aboard the Advanced Composition Explorer are reported over the energy range from ~100 to ~400 MeV nucleon^(–1). The propagation of cosmic rays through the Galaxy and heliosphere is modeled with constraints imposed by measurements. Isotopic source abundance ratios ^(31)P/^(32)S, ^(34)S/^(32)S, ^(38)Ar/^(36)Ar, and ^(44)Ca/^(40)Ca are deduced. The derived ^(31)P/^(32)S ratio is 2.34 ± 0.34 times larger than the solar system value, lending further credence to the suggestion that refractory elements are enriched in the GCRs due to the sputtering of ions off grains in the cores of superbubbles. By determining the GCR source abundances of argon (a noble gas) and calcium (a refractory), it is determined that material in grains is accelerated to GCR energies a factor of 6.4 ± 0.3 more efficiently than gas-phase material in this charge range. With this information, the dust fraction of phosphorus and sulfur in the interstellar material that is mixed with stellar ejecta to form the GCR seed material is found to be consistent with astronomical observations

Time-Dependent Synchrotron and Compton Spectra from Jets of Microquasars

Jet models for the high-energy emission of Galactic X-ray binary sources have regained significant interest with detailed spectral and timing studies of the X-ray emission from microquasars, the recent detection by the HESS collaboration of very-high-energy gamma-rays from the microquasar LS~5039, and the earlier suggestion of jet models for ultraluminous X-ray sources observed in many nearby galaxies. Here we study the synchrotron and Compton signatures of time-dependent electron injection and acceleration, adiabatic and radiative cooling, and different jet geometries in the jets of Galactic microquasars. Synchrotron, synchrotron-self-Compton, and external-Compton radiation processes with soft photons provided by the companion star and the accretion disk are treated. An analytical solution is presented to the electron kinetic equation for general power-law geometries of the jets for Compton scattering in the Thomson regime. We pay particular attention to predictions concerning the rapid flux and spectral variability signatures expected in a variety of scenarios, making specific predictions concerning possible spectral hysteresis, similar to what has been observed in several TeV blazars. Such predictions should be testable with dedicated monitoring observations of Galactic microquasars and ultraluminous X-ray sources using Chandra and/or XMM-Newton.Comment: Accepted for publication in ApJ; 37 manuscript pages, including 10 eps figures; uses AASTeX macro

Multi-wavelength constraints on cosmic-ray leptons in the Galaxy

Cosmic rays (CRs) interact with the gas, the radiation field and the magnetic field in the Milky Way, producing diffuse emission from radio to gamma rays. Observations of this diffuse emission and comparison with detailed predictions are powerful tools to unveil the CR properties and to study CR propagation. We present various GALPROP CR propagation scenarios based on current CR measurements. The predicted synchrotron emission is compared to radio surveys, and synchrotron temperature maps from WMAP and Planck, while the predicted interstellar gamma-ray emission is compared to Fermi-LAT observations. We show how multi-wavelength observations of the Galactic diffuse emission can be used to help constrain the CR lepton spectrum and propagation. Finally we discuss how radio and microwave data could be used in understanding the diffuse Galactic gamma-ray emission observed with Fermi-LAT, especially at low energies.Comment: 8 pages, 5 figures; in Proceedings of the 34th International Cosmic Ray Conference (ICRC 2015), The Hague (The Netherlands); Oral contributio