A Hamiltonian functional for the linearized Einstein vacuum field equations

By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained.Comment: 5 pages, accepted in J. Phys.: Conf. Serie

Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty

We analyze the quantum dynamics of the non-relativistic two-dimensional isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken as toy model to analyze some of the various quantum theories that can be built from the application of Dirac's quantization rule to the various symplectic structures recently reported for this classical system. It is pointed out that that these quantum theories are inequivalent in the sense that the mean values for the operators (observables) associated with the same physical classical observable do not agree with each other. The inequivalence does not arise from ambiguities in the ordering of operators but from the fact of having several symplectic structures defined with respect to the same set of coordinates. It is also shown that the uncertainty relations between the fundamental observables depend on the particular quantum theory chosen. It is important to emphasize that these (somehow paradoxical) results emerge from the combination of two paradigms: Dirac's quantization rule and the usual Copenhagen interpretation of quantum mechanics.Comment: 8 pages, LaTex file, no figures. Accepted for publication in Phys. Rev.

Elasticity of highly cross-linked random networks

Starting from a microscopic model of randomly cross-linked particles with quenched disorder, we calculate the Laudau-Wilson free energy S for arbitrary cross-link densities. Considering pure shear deformations, S takes the form of the elastic energy of an isotropic amorphous solid state, from which the shear modulus can be identified. It is found to be an universal quantity, not depending on any microscopic length-scales of the model.Comment: 6 pages, 5 figure

Goldstone fluctuations in the amorphous solid state

Goldstone modes in the amorphous solid state, resulting from the spontaneous breaking of translational symmetry due to random localisation of particles, are discussed. Starting from a microscopic model with quenched disorder, the broken symmetry is identified to be that of relative translations of the replicas. Goldstone excitations, corresponding to pure shear deformations, are constructed from long wavelength distortions of the order parameter. The elastic free energy is computed, and it is shown that Goldstone fluctuations destroy localisation in two spatial dimensions, yielding a two-dimensional amorphous solid state characterised by power-law correlations.Comment: 7 pages, 2 figure

Charged particle dynamics in the presence of non-Gaussian L\'evy electrostatic fluctuations

Full orbit dynamics of charged particles in a $3$-dimensional helical magnetic field in the presence of $\alpha$-stable L\'evy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The L\'evy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of L\'evy fluctuations. The absolute value of the power law decay exponents are linearly proportional to the L\'evy index $\alpha$. The observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian L\'evy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.Comment: 5 pages, 5 figures. Accepted as a letter in Physics of Plasma

Random solids and random solidification: What can be learned by exploring systems obeying permanent random constraints?

In many interesting physical settings, such as the vulcanization of rubber, the introduction of permanent random constraints between the constituents of a homogeneous fluid can cause a phase transition to a random solid state. In this random solid state, particles are permanently but randomly localized in space, and a rigidity to shear deformations emerges. Owing to the permanence of the random constraints, this phase transition is an equilibrium transition, which confers on it a simplicity (at least relative to the conventional glass transition) in the sense that it is amenable to established techniques of equilibrium statistical mechanics. In this Paper I shall review recent developments in the theory of random solidification for systems obeying permanent random constraints, with the aim of bringing to the fore the similarities and differences between such systems and those exhibiting the conventional glass transition. I shall also report new results, obtained in collaboration with Weiqun Peng, on equilibrium correlations and susceptibilities that signal the approach of the random solidification transition, discussing the physical interpretation and values of these quantities both at the Gaussian level of approximation and, via a renormalization-group approach, beyond.Comment: Paper presented at the "Unifying Concepts in Glass Physics" workshop, International Centre for Theoretical Physics, Trieste, Italy (September 15-18, 1999

Time reparametrization invariance in arbitrary range p-spin models: symmetric versus non-symmetric dynamics

We explore the existence of time reparametrization symmetry in p-spin models. Using the Martin-Siggia-Rose generating functional, we analytically probe the long-time dynamics. We perform a renormalization group analysis where we systematically integrate over short timescale fluctuations. We find three families of stable fixed points and study the symmetry of those fixed points with respect to time reparametrizations. One of those families is composed entirely of symmetric fixed points, which are associated with the low temperature dynamics. The other two families are composed entirely of non-symmetric fixed points. One of these two non-symmetric families corresponds to the high temperature dynamics. Time reparametrization symmetry is a continuous symmetry that is spontaneously broken in the glass state and we argue that this gives rise to the presence of Goldstone modes. We expect the Goldstone modes to determine the properties of fluctuations in the glass state, in particular predicting the presence of dynamical heterogeneity.Comment: v2: Extensively modified to discuss both high temperature (non-symmetric) and low temperature (symmetric) renormalization group fixed points. Now 16 pages with 1 figure. v1: 13 page

Early-expressed chemokines predict kidney immunopathology in experimental disseminated Candida albicans infections

Available under the Creative Commons Attribution License (CCAL)Peer reviewedPublisher PD

Molecular Gas, Dust and Star Formation in Galaxies: II. Dust properties and scalings in \sim\ 1600 nearby galaxies

We aim to characterize the relationship between dust properties. We also aim to provide equations to estimate accurate dust properties from limited observational datasets. We assemble a sample of 1,630 nearby (z<0.1) galaxies-over a large range of Mstar, SFR - with multi-wavelength observations available from wise, iras, planck and/or SCUBA. The characterization of dust emission comes from SED fitting using Draine & Li dust models, which we parametrize using two components (warm and cold ). The subsample of these galaxies with global measurements of CO and/or HI are used to explore the molecular and/or atomic gas content of the galaxies. The total Lir, Mdust and dust temperature of the cold component (Tc) form a plane that we refer to as the dust plane. A galaxy's sSFR drives its position on the dust plane: starburst galaxies show higher Lir, Mdust and Tc compared to Main Sequence and passive galaxies. Starburst galaxies also show higher specific Mdust (Mdust/Mstar) and specific Mgas (Mgas/Mstar). The Mdust is more closely correlated with the total Mgas (atomic plus molecular) than with the individual components. Our multi wavelength data allows us to define several equations to estimate Lir, Mdust and Tc from one or two monochromatic luminosities in the infrared and/or sub-millimeter. We estimate the dust mass and infrared luminosity from a single monochromatic luminosity within the R-J tail of the dust emission, with errors of 0.12 and 0.20dex, respectively. These errors are reduced to 0.05 and 0.10 dex, respectively, if the Tc is used. The Mdust is correlated with the total Mism (Mism \propto Mdust^0.7). For galaxies with Mstar 8.5<log(Mstar/Msun) < 11.9, the conversion factor \alpha_850mum shows a large scatter (rms=0.29dex). The SF mode of a galaxy shows a correlation with both the Mgass and Mdust: high Mdust/Mstar galaxies are gas-rich and show the highest SFRs.Comment: 24 pages, 28 figures, 6 tables, Accepted for publication in A&