Stochastic interpretation of Kadanoff-Baym equations and their relation to Langevin processes

In this more pedagogical study we want to elucidate on stochastic aspects inherent to the (non-)equilibrium real time Green's function description (or `closed time path Green's function' -- CTPGF) of transport equations, the so called `Kadanoff-Baym equations'. As a toy model we couple a free scalar boson quantum field to an exemplaric heat bath with some given temperature T. It will be shown in detail that the emerging transport equations have to be understood as the ensemble average over stochastic equations of Langevin type. This corresponds to the equivalence of the influence functional approach by Feynman and Vernon and the CTP technique. The former, however, gives a more intuitive physical picture. In particular the physical role of (quantum) noise and the connection of its correlation kernel to the Kadanoff-Baym equations will be discussed. The inherent presence of noise and dissipation related by the fluctuation-dissipation theorem guarantees that the modes or particles become thermally populated on average in the long-time limit. For long wavelength modes with momenta much less than the temperature the emerging wave equation do behave nearly as classical. On the other hand, a kinetic transport description can be obtained in the semi-classical particle regime. Including fluctuations, its form resembles that of a phenomenological Boltzmann-Langevin description. However, we will point out some severe discrepancies in comparison to the Boltzmann- Langevin scheme. As a further byproduct we also note how the occurrence of so called pinch singularities is circumvented by a clear physical necessity of damping within the one-particle propagator.Comment: 57 pages, Revtex, 2 figure

New light on gamma-ray burst host galaxies with Herschel

Until recently, dust emission has been detected in very few host galaxies of gamma-ray bursts (GRBHs). With Herschel, we have now observed 17 GRBHs up to redshift z~3 and detected seven of them at infrared (IR) wavelengths. This relatively high detection rate (41%) may be due to the composition of our sample which at a median redshift of 1.1 is dominated by the hosts of dark GRBs. Although the numbers are small, statistics suggest that dark GRBs are more likely to be detected in the IR than their optically-bright counterparts. Combining our IR data with optical, near-infrared, and radio data from our own datasets and from the literature, we have constructed spectral energy distributions (SEDs) which span up to 6 orders of magnitude in wavelength. By fitting the SEDs, we have obtained stellar masses, dust masses, star-formation rate (SFR), and extinctions for our sample galaxies. We find that GRBHs are galaxies that tend to have a high specfic SFR (sSFR), and like other star-forming galaxies, their ratios of dust-to-stellar mass are well correlated with sSFR. We incorporate our Herschel sample into a larger compilation of GRBHs, and compare this combined sample to SFR-weighted median stellar masses of the widest, deepest galaxy survey to date. This is done in order to establish whether or not GRBs can be used as an unbiased tracer of cosmic comoving SFR density (SFRD) in the universe. In contrast with previous results, this comparison shows that GRBHs are medium-sized galaxies with relatively high sSFRs; stellar masses and sSFRs of GRBHs as a function of redshift are similar to what is expected for star-forming galaxy populations at similar redshifts. We conclude that there is no strong evidence that GRBs are biased tracers of SFRD; thus they should be able to reliably probe the SFRD to early epochs.Comment: 18 pages, 9 figures, accepted for publication in A&A. Revised to include Fig. 6, mistakenly omitted in origina

Configuration mixing in 188^{188}Pb : band structure and electromagnetic properties

In the present paper, we carry out a detailed analysis of the presence and mixing of various families of collective bands in $^{188}$Pb. Making use of the interacting boson model, we construct a particular intermediate basis that can be associated with the unperturbed bands used in more phenomenological studies. We use the E2 decay to construct a set of collective bands and discuss in detail the B(E2)-values. We also perform an analysis of these theoretical results (Q, B(E2)) to deduce an intrinsic quadrupole moment and the associated quadrupole deformation parameter, using an axially deformed rotor model.Comment: submitted to pr

One-loop energy-momentum tensor in QED with electric-like background

We have obtained nonperturbative one-loop expressions for the mean energy-momentum tensor and current density of Dirac's field on a constant electric-like background. One of the goals of this calculation is to give a consistent description of back-reaction in such a theory. Two cases of initial states are considered: the vacuum state and the thermal equilibrium state. First, we perform calculations for the vacuum initial state. In the obtained expressions, we separate the contributions due to particle creation and vacuum polarization. The latter contributions are related to the Heisenberg-Euler Lagrangian. Then, we study the case of the thermal initial state. Here, we separate the contributions due to particle creation, vacuum polarization, and the contributions due to the work of the external field on the particles at the initial state. All these contributions are studied in detail, in different regimes of weak and strong fields and low and high temperatures. The obtained results allow us to establish restrictions on the electric field and its duration under which QED with a strong constant electric field is consistent. Under such restrictions, one can neglect the back-reaction of particles created by the electric field. Some of the obtained results generalize the calculations of Heisenberg-Euler for energy density to the case of arbitrary strong electric fields.Comment: 35 pages; misprints in the sign in definitions (40)-(43), and (68) corrected, results unchange

A reduced-order strategy for 4D-Var data assimilation

This paper presents a reduced-order approach for four-dimensional variational data assimilation, based on a prior EO F analysis of a model trajectory. This method implies two main advantages: a natural model-based definition of a mul tivariate background error covariance matrix $\textbf{B}_r$, and an important decrease of the computational burden o f the method, due to the drastic reduction of the dimension of the control space. % An illustration of the feasibility and the effectiveness of this method is given in the academic framework of twin experiments for a model of the equatorial Pacific ocean. It is shown that the multivariate aspect of $\textbf{B}_r$ brings additional information which substantially improves the identification procedure. Moreover the computational cost can be decreased by one order of magnitude with regard to the full-space 4D-Var method

The Star Formation Rate in the Reionization Era as Indicated by Gamma-ray Bursts

High-redshift gamma-ray bursts (GRBs) offer an extraordinary opportunity to study aspects of the early Universe, including the cosmic star formation rate (SFR). Motivated by the two recent highest-z GRBs, GRB 080913 at z = 6.7 and GRB 090423 at z = 8.1, and more than four years of Swift observations, we first confirm that the GRB rate does not trace the SFR in an unbiased way. Correcting for this, we find that the implied SFR to beyond z = 8 is consistent with LBG-based measurements after accounting for unseen galaxies at the faint end of the UV luminosity function. We show that this provides support for the integrated star formation in the range 6 < z < 8 to have been alone sufficient to reionize the Universe.Comment: 4 pages, 4 figures; modified to match version accepted for publication in ApJ Letter

Quasiparticle excitations in relativistic quantum field theory

We analyze the particle-like excitations arising in relativistic field theories in states different than the vacuum. The basic properties characterizing the quasiparticle propagation are studied using two different complementary methods. First we introduce a frequency-based approach, wherein the quasiparticle properties are deduced from the spectral analysis of the two-point propagators. Second, we put forward a real-time approach, wherein the quantum state corresponding to the quasiparticle excitation is explicitly constructed, and the time-evolution is followed. Both methods lead to the same result: the energy and decay rate of the quasiparticles are determined by the real and imaginary parts of the retarded self-energy respectively. Both approaches are compared, on the one hand, with the standard field-theoretic analysis of particles in the vacuum and, on the other hand, with the mean-field-based techniques in general backgrounds.Comment: 53 pages, 4 figures. Version accepted for publication in Ann. Phy

Evaporation of the gluon condensate: a model for pure gauge SU(3)_c phase transition

We interpret lattice data for the equation of state of pure gauge $SU(3)_c$ by an evaporation model. At low temperatures gluons are frozen inside the gluon condensate, whose dynamics is described in terms of a dilaton lagrangian. Above the critical temperature quasi-free gluons evaporate from the condensate: a first order transition is obtained by minimizing the thermodynamical potential of the system. Within the model it is possible to reproduce lattice QCD results at finite temperature for thermodynamical quantities such as pressure and energy. The gluonic longitudinal mass can also be evaluated; it vanishes below the critical temperature, where it shows a discontinuity. At very large temperatures we recover the perturbative scenario and gluons are the only asymptotic degrees of freedom.Comment: 21 pages, 8 figures. Expanded version including a discussion of the asymptotic degrees of freedom and of the gluon mas

Superconductivity close to the Mott state: From condensed-matter systems to superfluidity in optical lattices

Since the discovery of high-temperature superconductivity in 1986 by Bednorz and Mueller, great efforts have been devoted to finding out how and why it works. From the d-wave symmetry of the order parameter, the importance of antiferromagnetic fluctuations, and the presence of a mysterious pseudogap phase close to the Mott state, one can conclude that high-Tc superconductors are clearly distinguishable from the well-understood BCS superconductors. The d-wave superconducting state can be understood through a Gutzwiller-type projected BCS wave-function. In this review article, we revisit the Hubbard model at half-filling and focus on the emergence of exotic superconductivity with d-wave symmetry in the vicinity of the Mott state, starting from ladder systems and then studying the dimensional crossovers to higher dimensions. This allows to confirm that short-range antiferromagnetic fluctuations can mediate superconductivity with d-wave symmetry. Ladders are also nice prototype systems allowing to demonstrate the truncation of the Fermi surface and the emergence of a Resonating Valence Bond (RVB) state with preformed pairs in the vicinity of the Mott state. In two dimensions, a similar scenario emerges from renormalization group arguments. We also discuss theoretical predictions for the d-wave superconducting phase as well as the pseudogap phase, and address the crossover to the overdoped regime. Finally, cold atomic systems with tunable parameters also provide a complementary insight into this outstanding problem.Comment: 98 pages and 18 figures; Final version (references added and misprints corrected

The first Infrared study of the close environment of a long Gamma-Ray Burst

We present a characterization of the close environment of GRB980425 based on 5-160mic spectro-imaging obtained with Spitzer. The Gamma-Ray Burst GRB980425 occurred in a nearby (z=0.0085) SBc-type dwarf galaxy, at a projected distance of 900pc from an HII region with strong signatures of Wolf-Rayet (WR) stars. While this "WR region" produces less than 5% of the B-band emission of the host, we find that it is responsible for 45+/-10% of the total infrared luminosity, with a maximum contribution reaching 75% at 25-30mic. This atypical property is rarely observed among morphologically-relaxed dwarves, suggesting a strong causal link with the GRB event. The luminosity of the WR region (L_8-1000mic=4.6x10^8 Lsol), the peak of its spectral energy distribution at <~100mic and the presence of highly-ionized emission lines (e.g., [NeIII]) also reveal extremely young (<5Myr) star-forming activity, with a typical time-scale of only 47Myr to double the stellar mass already built. Finally, the mid-IR over B-band luminosity ratio in this region is substantially higher than in star-forming galaxies with similar L_IR, but it is lower than in young dust-enshrouded stellar clusters. Considering the modest obscuration measured from the silicate features (tau_9.7mic ~ 0.015), this suggests that the WR region is dominated by one or several star clusters that have either partly escaped or cleared out their parent molecular cloud. Combined with the properties characterizing the whole population of GRB hosts, our results reinforce the idea that long GRBs mostly happen within or in the vicinity of relatively unobscured galactic regions harboring very recent star formation.Comment: ApJ in press, 14 pages, 2 tables, 7 figure