Solution of the Dyson--Schwinger equation on de Sitter background in IR limit

We propose an ansatz which solves the Dyson-Schwinger equation for the real scalar fields in Poincare patch of de Sitter space in the IR limit. The Dyson-Schwinger equation for this ansatz reduces to the kinetic equation, if one considers scalar fields from the principal series. Solving the latter equation we show that under the adiabatic switching on and then off the coupling constant the Bunch-Davies vacuum relaxes in the future infinity to the state with the flat Gibbons-Hawking density of out-Jost harmonics on top of the corresponding de Sitter invariant out-vacuum.Comment: 20 pages, including 4 pages of Appendix. Acknowledgements correcte

Free zero-range processes on networks

A free zero-range process (FRZP) is a simple stochastic process describing the dynamics of a gas of particles hopping between neighboring nodes of a network. We discuss three different cases of increasing complexity: (a) FZRP on a rigid geometry where the network is fixed during the process, (b) FZRP on a random graph chosen from a given ensemble of networks, (c) FZRP on a dynamical network whose topology continuously changes during the process in a way which depends on the current distribution of particles. The case (a) provides a very simple realization of the phenomenon of condensation which manifests as the appearance of a condensate of particles on the node with maximal degree. The case (b) is very interesting since the averaging over typical ensembles of graphs acts as a kind of homogenization of the system which makes all nodes identical from the point of view of the FZRP. In the case (c), the distribution of particles and the dynamics of network are coupled to each other. The strength of this coupling depends on the ratio of two time scales: for changes of the topology and of the FZRP. We will discuss a specific example of that type of interaction and show that it leads to an interesting phase diagram.Comment: 11 pages, 4 figures, to appear in Proceedings of SPIE Symposium "Fluctuations and Noise 2007", Florence, 20-24 May 200

Balls-in-boxes condensation on networks

We discuss two different regimes of condensate formation in zero-range processes on networks: on a q-regular network, where the condensate is formed as a result of a spontaneous symmetry breaking, and on an irregular network, where the symmetry of the partition function is explicitly broken. In the latter case we consider a minimal irregularity of the q-regular network introduced by a single Q-node with degree Q>q. The statics and dynamics of the condensation depends on the parameter log(Q/q), which controls the exponential fall-off of the distribution of particles on regular nodes and the typical time scale for melting of the condensate on the Q-node which increases exponentially with the system size $N$. This behavior is different than that on a q-regular network where log(Q/q)=0 and where the condensation results from the spontaneous symmetry breaking of the partition function, which is invariant under a permutation of particle occupation numbers on the q-nodes of the network. In this case the typical time scale for condensate melting is known to increase typically as a power of the system size.Comment: 7 pages, 3 figures, submitted to the "Chaos" focus issue on "Optimization in Networks" (scheduled to appear as Volume 17, No. 2, 2007

Asymmetric correlation matrices: an analysis of financial data

We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson correlation matrices to the realm of complex eigenvalues. We employ some recent random matrix theory results on the average eigenvalue density of this type of matrices to distinguish between noise and non trivial correlation structures, and we focus on financial data as a case study. Namely, we employ daily prices of stocks belonging to the American and British stock exchanges, and look for the emergence of correlations between two such markets in the eigenvalue spectrum of their non symmetric correlation matrix. We find several non trivial results, also when considering time-lagged correlations over short lags, and we corroborate our findings by additionally studying the asymmetric correlation matrix of the principal components of our datasets.Comment: Revised version; 11 pages, 13 figure

Quantum widening of CDT universe

The physical phase of Causal Dynamical Triangulations (CDT) is known to be described by an effective, one-dimensional action in which three-volumes of the underlying foliation of the full CDT play a role of the sole degrees of freedom. Here we map this effective description onto a statistical-physics model of particles distributed on 1d lattice, with site occupation numbers corresponding to the three-volumes. We identify the emergence of the quantum de-Sitter universe observed in CDT with the condensation transition known from similar statistical models. Our model correctly reproduces the shape of the quantum universe and allows us to analytically determine quantum corrections to the size of the universe. We also investigate the phase structure of the model and show that it reproduces all three phases observed in computer simulations of CDT. In addition, we predict that two other phases may exists, depending on the exact form of the discretised effective action and boundary conditions. We calculate various quantities such as the distribution of three-volumes in our model and discuss how they can be compared with CDT.Comment: 19 pages, 13 figure

Random matrix model for QCD_3 staggered fermions

We show that the lowest part of the eigenvalue density of the staggered fermion operator in lattice QCD_3 at small lattice coupling constant beta has exactly the same shape as in QCD_4. This observation is quite surprising, since universal properties of the QCD_3 Dirac operator are expected to be described by a non-chiral matrix model. We show that this effect is related to the specific nature of the staggered fermion discretization and that the eigenvalue density evolves towards the non-chiral random matrix prediction when beta is increased and the continuum limit is approached. We propose a two-matrix model with one free parameter which interpolates between the two limits and very well mimics the pattern of evolution with beta of the eigenvalue density of the staggered fermion operator in QCD_3.Comment: 8 pages 4 figure

Electron dynamics in gold and gold–silver alloy nanoparticles: The influence of a nonequilibrium electron distribution and the size dependence of the electron–phonon relaxation

©1999 American Institute of Physics. The electronic version of this article is the complete one and can be found online at: http://link.aip.org/link/?JCPSA6/111/1255/1DOI: 10.1063/1.479310Electron dynamics in gold nanoparticles with an average diameter between 9 and 48 nm have been studied by femtosecond transient absorption spectroscopy. Following the plasmon bleach recovery after low power excitation indicates that a non-Fermi electron distribution thermalizes by electron–electron relaxation on a time scale of 500 fs to a Fermi distribution. This effect is only observed at low excitation power and when the electron distribution is perturbed by mixing with the intraband transitions within the conduction band (i.e., when the excitation wavelength is 630 or 800 nm). However, exciting the interband transitions at 400 nm does not allow following the early electron thermalization process. Electron thermalization with the lattice of the nanoparticle by electron–phonon interactions occurs within 1.7 ps under these conditions, independent of the excitation wavelength. In agreement with the experiments, simulations of the optical response arising from thermalized and nonthermalized electron distributions show that a non-Fermi electron distribution leads to a less intense bleach of the plasmon absorption. Furthermore, the difference between the response from the two electron distributions is greater for small temperature changes of the electron gas (low excitation powers). No size dependence of the electron thermalization dynamics is observed for gold nanoparticles with diameters between 9 and 48 nm. High-resolution transmission electron microscopy (HRTEM) reveals that these gold nanoparticles possess defect structures. The effect of this on the electron–phonon relaxation processes is discussed. 18 nm gold–silver alloy nanoparticles with a gold mole fraction of 0.8 are compared to 15 nm gold nanoparticles. While mixing silver leads to a blue-shift of the plasmon absorption in the ground-state absorption spectrum, no difference is observed in the femtosecond dynamics of the system