Bulk Viscosity of Interacting Hadrons

We show that first approximations to the bulk viscosity $\eta_v$ are expressible in terms of factors that depend on the sound speed $v_s$, the enthalpy, and the interaction (elastic and inelastic) cross section. The explicit dependence of $\eta_v$ on the factor $(\frac 13 - v_s^2)$ is demonstrated in the Chapman-Enskog approximation as well as the variational and relaxation time approaches. The interesting feature of bulk viscosity is that the dominant contributions at a given temperature arise from particles which are neither extremely nonrelativistic nor extremely relativistic. Numerical results for a model binary mixture are reported.Comment: 4 pages, 1 figure, Contribution to Quark Matter 2009, Knoxville, Tennessee, US

Probing the basins of attraction of a recurrent neural network

A recurrent neural network is considered that can retrieve a collection of patterns, as well as slightly perturbed versions of this `pure' set of patterns via fixed points of its dynamics. By replacing the set of dynamical constraints, i.e., the fixed point equations, by an extended collection of fixed-point-like equations, analytical expressions are found for the weights w_ij(b) of the net, which depend on a certain parameter b. This so-called basin parameter b is such that for b=0 there are, a priori, no perturbed patterns to be recognized by the net. It is shown by a numerical study, via probing sets, that a net constructed to recognize perturbed patterns, i.e., with values of the connections w_ij(b) with b unequal zero, possesses larger basins of attraction than a net made with the help of a pure set of patterns, i.e., with connections w_ij(b=0). The mathematical results obtained can, in principle, be realized by an actual, biological neural net.Comment: 17 pages, LaTeX, 2 figure

First-principles nonequilibrium Green's function approach to transient photoabsorption: Application to atoms

We put forward a first-principle NonEquilibrium Green's Function (NEGF) approach to calculate the transient photoabsorption spectrum of optically thin samples. The method can deal with pump fields of arbitrary strength, frequency and duration as well as for overlapping and nonoverlapping pump and probe pulses. The electron-electron repulsion is accounted for by the correlation self-energy, and the resulting numerical scheme deals with matrices that scale quadratically with the system size. Two recent experiments, the first on helium and the second on krypton, are addressed. For the first experiment we explain the bending of the Autler-Townes absorption peaks with increasing the pump-probe delay \t, and relate the bending to the thickness and density of the gas. For the second experiment we find that sizable spectral structures of the pump-generated admixture of Kr ions are fingerprints of {\em dynamical correlation} effects, and hence they cannot be reproduced by time-local self-energy approximations. Remarkably, the NEGF approach also captures the retardation of the absorption onset of Kr$^{2+}$ with respect to Kr$^{1+}$ as a function of \t.Comment: 13 pages, 8 captioned figure

Ultra-nonlocality in density functional theory for photo-emission spectroscopy

We derive an exact expression for the photo-current of photo-emission spectroscopy using time-dependent current density functional theory (TDCDFT). This expression is given as an integral over the Kohn-Sham spectral function renormalized by effective potentials that depend on the exchange-correlation kernel of current density functional theory. We analyze in detail the physical content of this expression by making a connection between the density-functional expression and the diagrammatic expansion of the photo-current within many-body perturbation theory. We further demonstrate that the density functional expression does not provide us with information on the kinetic energy distribution of the photo-electrons. Such information can, in principle, be obtained from TDCDFT by exactly modeling the experiment in which the photo-current is split into energy contributions by means of an external electromagnetic field outside the sample, as is done in standard detectors. We find, however, that this procedure produces very nonlocal correlations between the exchange-correlation fields in the sample and the detector.Comment: 11 pages, 11 figure

Diagrammatic expansion for positive density-response spectra: Application to the electron gas

In a recent paper [Phys. Rev. B 90, 115134 (2014)] we put forward a diagrammatic expansion for the self-energy which guarantees the positivity of the spectral function. In this work we extend the theory to the density response function. We write the generic diagram for the density-response spectrum as the sum of partitions. In a partition the original diagram is evaluated using time-ordered Green's functions (GF) on the left-half of the diagram, antitime-ordered GF on the right-half of the diagram and lesser or greater GF gluing the two halves. As there exist more than one way to cut a diagram in two halves, to every diagram corresponds more than one partition. We recognize that the most convenient diagrammatic objects for constructing a theory of positive spectra are the half-diagrams. Diagrammatic approximations obtained by summing the squares of half-diagrams do indeed correspond to a combination of partitions which, by construction, yield a positive spectrum. We develop the theory using bare GF and subsequently extend it to dressed GF. We further prove a connection between the positivity of the spectral function and the analytic properties of the polarizability. The general theory is illustrated with several examples and then applied to solve the long-standing problem of including vertex corrections without altering the positivity of the spectrum. In fact already the first-order vertex diagram, relevant to the study of gradient expansion, Friedel oscillations, etc., leads to spectra which are negative in certain frequency domain. We find that the simplest approximation to cure this deficiency is given by the sum of the zero-th order bubble diagram, the first-order vertex diagram and a partition of the second-order ladder diagram. We evaluate this approximation in the 3D homogeneous electron gas and show the positivity of the spectrum for all frequencies and densities.Comment: 19 pages, 19 figure

Diagrammatic expansion for positive spectral functions beyond GW: Application to vertex corrections in the electron gas

We present a diagrammatic approach to construct self-energy approximations within many-body perturbation theory with positive spectral properties. The method cures the problem of negative spectral functions which arises from a straightforward inclusion of vertex diagrams beyond the GW approximation. Our approach consists of a two-steps procedure: we first express the approximate many-body self-energy as a product of half-diagrams and then identify the minimal number of half-diagrams to add in order to form a perfect square. The resulting self-energy is an unconventional sum of self-energy diagrams in which the internal lines of half a diagram are time-ordered Green's functions whereas those of the other half are anti-time-ordered Green's functions, and the lines joining the two halves are either lesser or greater Green's functions. The theory is developed using noninteracting Green's functions and subsequently extended to self-consistent Green's functions. Issues related to the conserving properties of diagrammatic approximations with positive spectral functions are also addressed. As a major application of the formalism we derive the minimal set of additional diagrams to make positive the spectral function of the GW approximation with lowest-order vertex corrections and screened interactions. The method is then applied to vertex corrections in the three-dimensional homogeneous electron gas by using a combination of analytical frequency integrations and numerical Monte-Carlo momentum integrations to evaluate the diagrams.Comment: 19 pages, 19 figure

Vertex corrections for positive-definite spectral functions of simple metals

We present a systematic study of vertex corrections in the homogeneous electron gas at metallic densities. The vertex diagrams are built using a recently proposed positive-definite diagrammatic expansion for the spectral function. The vertex function not only provides corrections to the well known plasmon and particle-hole scatterings, but also gives rise to new physical processes such as generation of two plasmon excitations or the decay of the one-particle state into a two-particles-one-hole state. By an efficient Monte Carlo momentum integration we are able to show that the additional scattering channels are responsible for the bandwidth reduction observed in photoemission experiments on bulk sodium, appearance of the secondary plasmon satellite below the Fermi level, and a substantial redistribution of spectral weights. The feasibility of the approach for first-principles band-structure calculations is also discussed

Conserving Approximations in Time-Dependent Density Functional Theory

In the present work we propose a theory for obtaining successively better approximations to the linear response functions of time-dependent density or current-density functional theory. The new technique is based on the variational approach to many-body perturbation theory (MBPT) as developed during the sixties and later expanded by us in the mid nineties. Due to this feature the resulting response functions obey a large number of conservation laws such as particle and momentum conservation and sum rules. The quality of the obtained results is governed by the physical processes built in through MBPT but also by the choice of variational expressions. We here present several conserving response functions of different sophistication to be used in the calculation of the optical response of solids and nano-scale systems.Comment: 11 pages, 4 figures, revised versio

3D FEM Simulations of a shape rolling process

A finite element model has been developed for the simulation of the shape rolling of stator\ud vanes. These simulations should support the design of rolling tools for new vane types. For the time being\ud only straight vanes (vanes with a constant cross-section over the length) are studied. In that case the rolling\ud process can be considered stationary and an ALE formulation is suitable to calculate the steady state. Results\ud of simulations and experiments for a symmetrical straight vane are presente