Relativistic Diffusion Model Research Articles

Particle production and nonlinear diffusion in relativistic systems

AbstractThe short parton production phase in high‐energy heavy‐ion collisions is treated analytically as a nonlinear diffusion process. The initial buildup of the rapidity density distributions of produced charged hadrons within τp≃ 0.25 fm/c occurs in three sources during the colored partonic phase. In a two‐step approach, the subsequent diffusion in pseudorapidity space during the interaction time of τint≃ 7‐10 fm/c (mean duration of the collision) is essentially linear as expressed in the Relativistic Diffusion Model (RDM) which yields excellent agreement with the data at RHIC energies, and allows for predictions at LHC energies. Results for d+Au are discussed in detail.

Particle production and nonlinear diffusion in relativistic systems

The short parton production phase in high-energy heavy-ion collisions is treated analytically as a nonlinear diffusion process. The initial buildup of the rapidity density distributions of produced charged hadrons within tau_p = 0.25 fm/c occurs in three sources during the colored partonic phase. In a two-step approach, the subsequent diffusion in pseudorapidity space during the interaction time of tau_int = 7-10 fm/c (mean duration of the collision) is essentially linear as expressed in the Relativistic Diffusion Model (RDM) which yields excellent agreement with the data at RHIC energies, and allows for predictions at LHC energies. Results for d+Au are discussed in detail.

Diffusion or bounce back in relativistic heavy-ion collisions?

The time evolution of pseudorapidity distributions of produced charged hadrons in d + Au collisions at $ \sqrt{{s_{NN}}}$ = 200 GeV is investigated. Results of a nonequilibrium statistical relativistic diffusion model with three sources are compared with a macroscopic “bounce-back” model that does not allow for statistical equilibration at large times, but instead leads to motion reversal. When compared to the data, the results of the diffusion approach are more precise, thus emphasizing that the system is observed to be on its way to thermal equilibrium.

From RHIC to LHC: a relativistic diffusion approach

We investigate stopping and particle production in heavy-ion collisions in a Relativistic Diffusion Model (RDM). Using three sources for particle production, the energy- and centrality dependence of rapidity distributions of net protons, and pseudorapidity distributions of charged hadrons in heavy systems at RHIC energies are precisely reproduced in the analytical model. The transport coefficients are then extrapolated from Au + Au at RHIC energies (OsNN=19.6 - 200 GeV) to Pb + Pb at LHC energies of OsNN= 5.52 TeV. Rapidity distributions for net protons, and pseudorapidity spectra for produced charged particles are obtained and discussed in a three-sources model at LHC energies.

From RHIC to LHC: A relativistic diffusion approach

Stopping and particle production in heavy-ion collisions are investigated in a Relativistic Diffusion Model (RDM). Using three sources for particle production, the energy- and centrality dependence of rapidity distributions of net protons, and pseudorapidity distributions of charged hadrons in heavy systems at RHIC energies are precisely reproduced in the analytical model. The gradual approach to local thermal equilibrium is discussed. The transport coefficients are then extrapolated from Au + Au at RHIC energies ( s N N = 19.6 − 200 GeV ) to Pb + Pb at LHC energies of s N N = 5.52 TeV . Rapidity distributions fot net protons, and pseudorapidity spectra for produced charged particles are obtained and discussed in a three-sources model at LHC energies.

Relativistic diffusion processes and random walk models

The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As is well known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equation, whose solutions avoid superluminal propagation speeds but suffer from singular (noncontinuous) diffusion fronts on the light cone, which are unlikely to exist for massive particles. It is therefore advisable to explore other alternatives as well. In this paper, a generalized Wiener process is proposed that is continuous, avoids superluminal propagation, and reduces to the standard Wiener process in the nonrelativistic limit. The corresponding relativistic diffusion propagator is obtained directly from the nonrelativistic Wiener propagator, by rewriting the latter in terms of an integral over actions. The resulting relativistic process is non-Markovian, in accordance with the known fact that nontrivial continuous, relativistic Markov processes in position space cannot exist. Hence, the proposed process defines a consistent relativistic diffusion model for massive particles and provides a viable alternative to the solutions of the telegraph equation.

Editorial:John Wiley & Sons, 1807–2007: 200 years success in publishing

We investigate the energy dependence of stopping and hadron production in high-energy heavy-ion collisions based on a three-sources Relativistic Diffusion Model. The transport coefficients are extrapolated from Au + Au and Cu + Cu at RHIC energies ( = 19.6–200 GeV) to Pb + Pb at LHC energies = 5.52 TeV. Rapidity distributions for net protons, and pseudorapidity spectra for produced charged particles in central collisions are compared to data at RHIC energies, and discussed for several extrapolations to LHC energies.

Diffusion in relativistic systems

Abstract A Relativistic Diffusion Model (RDM) for high-energy heavy-ion collisions is outlined and used to investigate stopping and particle production. With three sources for particle production, the energy- and centrality dependence of rapidity distributions of net protons, and pseudorapidity distributions of charged hadrons in heavy systems at RHIC energies are precisely reproduced in the analytical model. The gradual approach to local thermal equilibrium is discussed for symmetric and asymmetric (d+Au) systems. The transport coefficients are extrapolated from Au+Au at RHIC energies ( s N N = 19.6 – 200 GeV ) to Pb+Pb at LHC energies of s N N = 5.52 TeV . Rapidity distributions for net protons, and pseudorapidity spectra for the produced charged particles are obtained and discussed in a three-sources model at LHC energies.

From RHIC to LHC: a relativistic diffusion approach

AbstractWe investigate the energy dependence of stopping and hadron production in high‐energy heavy‐ion collisions based on a three‐sources Relativistic Diffusion Model. The transport coefficients are extrapolated from Au + Au and Cu + Cu at RHIC energies ( = 19.6–200 GeV) to Pb + Pb at LHC energies = 5.52 TeV. Rapidity distributions for net protons, and pseudorapidity spectra for produced charged particles in central collisions are compared to data at RHIC energies, and discussed for several extrapolations to LHC energies.

Rapidity equilibration in d + Au and Au + Au systems

In a Relativistic Diffusion Model (RDM), the evolution of net-proton rapidity spectra with $ \sqrt{{s_{NN}}}$ in heavy systems is proposed as an indicator for local equilibration and longitudinal expansion. The broad midrapidity valley recently discovered at RHIC in central Au + Au collisions at $ \sqrt{{s_{NN}}}$ = 200 GeV suggests rapid local equilibration which is most likely due to deconfinement, and fast longitudinal expansion. Rapidity spectra of produced charged hadrons in d + Au and Au + Au systems at RHIC energies and their centrality dependence are well described in a three-sources RDM. In central collisions, about 19% of the produced particles are in the equilibrated midrapidity region for d + Au.

Time evolution of relativistic d + Au and Au + Au collisions

AbstractThe evolution of charged‐particle production in collisions of heavy ions at relativistic energies is investigated as function of centrality in a nonequilibrium‐statistical framework. Precise agreement with recent d + Au and Au + Au data at = 200 GeV is found in a Relativistic Diffusion Model with three sources for particle production. Only the midrapidity source comes very close to local equilibrium, whereas the analyses of the overall pseudorapidity distributions show that the systems remain far from statistical equilibrium.

Diffusion and local deconfinement in relativistic systems

The evolution of net-proton rapidity spectra with s N N is heavy relativistic systems is proposed as an indicator for local equilibration, longitudinal expansion, and deconfinement. Bell-shaped distributions in central collisions at AGS energies and double-humped nonequilibrium spectra at SPS ishow substantial collective expansion. The broad midrapidity valley appearing at RHIC indicates longitudinal collective expansion of a locally equilibrated subsystem. In central Au-Au collisions at s N N = 200 GeV , fast local equilibration which is most likely due to deconfinement is estimated in a Relativistic Diffusion Model to occur for 14 per cent of the incoming baryons.

Diffusion and local deconfinement in relativistic systems

In relativistic heavy-ion systems at the highest collision energies, new deconfinement signatures emerge and indicate an increasingly clear separation between soft hadronic processes and hard partonic interactions in a locally deconfined subsystem. Here the emphasis is on longitudinal variables, namely, net-baryon rapidity distributions. As described in a Relativistic Diffusion Model, they change from bell shaped at the lower to double humped at the higher SPS energy, but do not reach local statistical equilibrium. At $\sqrt{{s}_{NN}}=200\phantom{\rule{0.3em}{0ex}}\text{GeV}$ in the Au-Au system, however, they are shown to consist of three components. In addition to the nonequilibrium contributions, a third fraction close to midrapidity containing ${Z}_{eq}\ensuremath{\simeq}22$ protons reaches local statistical equilibrium in a discontinuous transition. It may be associated with a deconfinement of the participant partons and thus, serve as a signature for quark-gluon matter formation.

Anomalous net-baryon-rapidity spectra at RHIC

Net-baryon rapidity distributions in central Au+Au collisions at sNN=200 GeV are shown to consist of three components. The nonequilibrium contributions are accounted for in a Relativistic Diffusion Model. Near midrapidity, a third fraction containing Zeq≃22 protons reaches local statistical equilibrium in a discontinuous transition. It may be associated with a deconfinement of the participant partons and thus, serve as a signature for Quark–Gluon Matter formation.