Theoretical understanding of the nuclear incompressibility: where do we stand ?

The status of the theoretical research on the compressional modes of finite nuclei and the incompressibility $K_\infty$ of nuclear matter, is reviewed. It is argued that the recent experimental data on the Isoscalar Giant Monopole Resonance (ISGMR) allow extracting the value of $K_\infty$ with an uncertainity of about $\pm$ 12 MeV. Non-relativistic (Skyrme, Gogny) and relativistic mean field models predict for $K_\infty$ values which are significantly different from one another, namely $\approx$ 220-235 and $\approx$ 250-270 MeV respectively. It is shown that the solution of this puzzle requires a better determination of the symmetry energy at, and around, saturation. The role played by the experimental data of the Isoscalar Giant Dipole Resonance (ISGDR) is also discussed.Comment: To appear in the proceedings of the COMEX1 conference (special issue of Nucl. Phys. A). Few changes and corrections compared to the previous version. General conclusion unchange

Long delay times in reaction rates increase intrinsic fluctuations

In spatially distributed cellular systems, it is often convenient to represent complicated auxiliary pathways and spatial transport by time-delayed reaction rates. Furthermore, many of the reactants appear in low numbers necessitating a probabilistic description. The coupling of delayed rates with stochastic dynamics leads to a probability conservation equation characterizing a non-Markovian process. A systematic approximation is derived that incorporates the effect of delayed rates on the characterization of molecular noise, valid in the limit of long delay time. By way of a simple example, we show that delayed reaction dynamics can only increase intrinsic fluctuations about the steady-state. The method is general enough to accommodate nonlinear transition rates, allowing characterization of fluctuations around a delay-induced limit cycle.Comment: 8 pages, 3 figures, to be published in Physical Review

Momentum conservation and correlation analyses in heavy-ion collisions at ultrarelativistic energies

Global transverse-momentum conservation induces correlations between any number of particles, which contribute in particular to the two- and three-particle correlations measured in heavy-ion collisions. These correlations are examined in detail, and their importance for studies of jets and their interaction with the medium is discussed.Comment: 5 pages, 2 figures. v2: corrected typos and added a paragrap

Transient rectification of Brownian diffusion with asymmetric initial distribution

In an ensemble of non-interacting Brownian particles, a finite systematic average velocity may temporarily develop, even if it is zero initially. The effect originates from a small nonlinear correction to the dissipative force, causing the equation for the first moment of velocity to couple to moments of higher order. The effect may be relevant when a complex system dissociates in a viscous medium with conservation of momentum

Statistics of 3-dimensional Lagrangian turbulence

We consider a superstatistical dynamical model for the 3-d movement of a Lagrangian tracer particle embedded in a high-Reynolds number turbulent flow. The analytical model predictions are in excellent agreement with recent experimental data for flow between counter-rotating disks. In particular, we calculate the Lagrangian scaling exponents zeta_j for our system, and show that they agree well with the measured exponents reported in [X. Hu et al., PRL 96, 114503 (2006)]. Moreover, the model correctly predicts the shape of velocity difference and acceleration probability densities, the fast decay of component correlation functions and the slow decay of the modulus, as well as the statistical dependence between acceleration components. Finally, the model explains the numerically [P.K. Yeung and S.B. Pope, J. Fluid Mech. 207, 531 (1989)] and experimentally observed fact [B.W. Zeff et al., Nature 421, 146 (2003)] that enstrophy lags behind dissipation.Comment: 5 pages, 3 figures. Replaced by final version accepted by Phys. Rev. Let

Multichannel calculation of excited vector ϕ\phi resonances and the ϕ(2170)\phi(2170)

A multichannel calculation of excited $J^{PC}=1^{--}$ $\phi$ states is carried out within a generalization of the Resonance-Spectrum Expansion, which may shed light on the classification of the $\phi(2170)$ resonance, discovered by BABAR and originally denoted X(2175). In this framework, a complete spectrum of bare $s\bar{s}$ states is coupled to those OZI-allowed decay channels that should be most relevant for the considered energy range. The included $S$- and $P$-wave two-meson channels comprise the lowest pseudoscalar, vector, scalar, and axial-vector mesons, while in the $q\bar{q}$ sector both the $^{3}S_1$ and $^{3}D_1$ states are coupled. The only two free parameters are tuned so as to reproduce mass and width of the $\phi(1020)$, but come out reasonably close to previously used values. Among the model's $T$-matrix poles, there are good candidates for observed resonances, as well other ones that should exist according to the quark model. Besides the expected resonances as unitarized confinement states, a dynamical resonance pole is found at $(2186-i246)$ MeV. The huge width makes its interpretation as the $\phi(2170)$ somewhat dubious, but further improvements of the model may change this conclusion.Comment: 6 pages, 5 figures, RevTex4; v2: very recent experimental result, some extra discussion, and 2 references added; v3: 3 new figures, 2 new equations, and some rephrasing; version accepted for publication in Phys. Rev.

A new modelling framework for statistical cumulus dynamics

We propose a new modelling framework suitable for the description of atmospheric convective systems as a collection of distinct plumes. The literature contains many examples of models for collections of plumes in which strong simplifying assumptions are made, a diagnostic dependence of convection on the large-scale environment and the limit of many plumes often being imposed from the outset. Some recent studies have sought to remove one or the other of those assumptions. The proposed framework removes both, and is explicitly time-dependent and stochastic in its basic character. The statistical dynamics of the plume collection are defined through simple probabilistic rules applied at the level of individual plumes, and van Kampen's system size expansion is then used to construct the macroscopic limit of the microscopic model. Through suitable choices of the microscopic rules, the model is shown to encompass previous studies in the appropriate limits, and to allow their natural extensions beyond those limits

Relaxation of finite perturbations: Beyond the Fluctuation-Response relation

We study the response of dynamical systems to finite amplitude perturbation. A generalized Fluctuation-Response relation is derived, which links the average relaxation toward equilibrium to the invariant measure of the system and points out the relevance of the amplitude of the initial perturbation. Numerical computations on systems with many characteristic times show the relevance of the above relation in realistic cases.Comment: 7 pages, 5 figure

Generalized Fokker-Planck equation, Brownian motion, and ergodicity

Microscopic theory of Brownian motion of a particle of mass $M$ in a bath of molecules of mass $m\ll M$ is considered beyond lowest order in the mass ratio $m/M$. The corresponding Langevin equation contains nonlinear corrections to the dissipative force, and the generalized Fokker-Planck equation involves derivatives of order higher than two. These equations are derived from first principles with coefficients expressed in terms of correlation functions of microscopic force on the particle. The coefficients are evaluated explicitly for a generalized Rayleigh model with a finite time of molecule-particle collisions. In the limit of a low-density bath, we recover the results obtained previously for a model with instantaneous binary collisions. In general case, the equations contain additional corrections, quadratic in bath density, originating from a finite collision time. These corrections survive to order $(m/M)^2$ and are found to make the stationary distribution non-Maxwellian. Some relevant numerical simulations are also presented

Reconciliation of a Quantum-Distributed Gaussian Key

Two parties, Alice and Bob, wish to distill a binary secret key out of a list of correlated variables that they share after running a quantum key distribution protocol based on continuous-spectrum quantum carriers. We present a novel construction that allows the legitimate parties to get equal bit strings out of correlated variables by using a classical channel, with as few leaked information as possible. This opens the way to securely correcting non-binary key elements. In particular, the construction is refined to the case of Gaussian variables as it applies directly to recent continuous-variable protocols for quantum key distribution.Comment: 8 pages, 4 figures. Submitted to the IEEE for possible publication. Revised version to improve its clarit