Quantized meson fields in and out of equilibrium. I : Kinetics of meson condensate and quasi-particle excitations
arXiv:0802.3496 · doi:10.1016/j.nuclphysa.2008.06.001
Abstract
We formulate a kinetic theory of self-interacting meson fields with an aim to describe the freezeout stage of the space-time evolution of matter in ultrarelativistic nuclear collisions. Kinetic equations are obtained from the Heisenberg equation of motion for a single component real scalar quantum field taking the mean field approximation for the non-linear interaction. The mesonic mean field obeys the classical non-linear Klein-Gordon equation with a modification due to the coupling to mesonic quasi-particle excitations which are expressed in terms of the Wigner functions of the quantum fluctuations of the meson field, namely the statistical average of the bilinear forms of the meson creation and annihilation operators. In the long wavelength limit, the equations of motion of the diagonal components of the Wigner functions take a form of Vlasov equation with a particle source and sink which arises due to the non-vanishing off-diagonal components of the Wigner function expressing coherent pair-creation and pair-annihilation process in the presence of non-uniform condensate. We show that in the static homogeneous system, these kinetic equations reduce to the well-known gap equation in the Hartree approximation, and hence they may be considered as a generalization of the Hartree approximation method to non-equilibrium systems. As an application of these kinetic equations, we compute the dispersion relations of the collective mesonic excitations in the system near equilibrium.
arXiv comment45 pages, 9 figurs
References in corpus (27)
- Experimental and Theoretical Challenges in the Search for the Quark Gluon Plasma: The STAR Collaboration's Critical Assessment of the Evidence from RHIC Collisions
- Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration
- The PHOBOS Perspective on Discoveries at RHIC
- QCD Phenomenology based on a Chiral Effective Lagrangian
- Femtoscopy in Relativistic Heavy Ion Collisions: Two Decades of Progress
- Chemical Equilibration in Pb+Pb Collisions at the SPS
- The Quark-Gluon Plasma: Collective Dynamics and Hard Thermal Loops
- Elliptic flow at SPS and RHIC: from kinetic transport to hydrodynamics
- Emergence of Coherent Long Wavelength Oscillations After a Quench: Application to QCD
- Apparent Thermalization due to Plasma Instabilities in Quark-Gluon Plasma
- Is early thermalization achieved only near midrapidity at RHIC ?
- Optimized Perturbation Theory at Finite Temperature
- Self-consistent Improvement of the Finite Temperature Effective Potential
- Anomalous Viscosity of an Expanding Quark-Gluon Plasma
- On the equivalence between the Boltzmann equation and classical field theory at large occupation numbers
- How to Make Large Domains of Disoriented Chiral Condensate
- How Disoriented Chiral Condensates Form: Quenching vs. Annealing
- Coupled Hartree-Fock-Bogoliubov kinetic equations for a trapped Bose gas
- Chiral Phase Transition at Finite Temperature in the Linear Sigma Model
- Finite temperature spectral functions of the linear O(N)-model at large N applied to the system
- Second sheet pole and the threshold enhancement of the spectral function in the scalar-isoscalar meson-sector
- Optimized Perturbation Theory at Finite Temperature--- Two-Loop Analysis---
- Momentum dependence of the spectral functions in the O(4) linear sigma model at finite temperature
- Mean field theory for collective motion of quantum meson fields
- Fundamental time asymmetry from nontrivial space topology
- Universal threshold enhancement
- Lifetime of Collective Isospin Rotations of a Quantum Meson Field