scholarly journals Landau–Pomeranchuk–Migdal effect in a quark–gluon plasma and the Boltzmann equation

2007 ◽  
Vol 644 (1) ◽  
pp. 48-53 ◽  
Author(s):  
Gordon Baym ◽  
J.-P. Blaizot ◽  
F. Gelis ◽  
T. Matsui
Keyword(s):  
Boltzmann Equation ◽  
Quark Gluon Plasma ◽  
Gluon Plasma ◽  
The Boltzmann Equation

The Boltzmann Equation and the H Theorem (1872–1875)

2018 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Heat Conduction ◽  
Boltzmann Equation ◽  
Transport Phenomena ◽  
Dilute Gas ◽  
The Boltzmann Equation ◽  
H Theorem ◽  
Irreversible Evolution

This chapter covers Boltzmann’s writings about the Boltzmann equation and the H theorem in the period 1872–1875, through which he succeeded in deriving the irreversible evolution of the distribution of molecular velocities in a dilute gas toward Maxwell’s distribution. Boltzmann also used his equation to improve on Maxwell’s theory of transport phenomena (viscosity, diffusion, and heat conduction). The bulky memoir of 1872 and the eponymous equation probably are Boltzmann’s most famous achievements. Despite the now often obsolete ways of demonstration, despite the lengthiness of the arguments, and despite hidden difficulties in the foundations, Boltzmann there displayed his constructive skills at their best.

Approach to Equilibrium, the H-Theorem and Irreversibility

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Boltzmann Equation ◽  
Detailed Knowledge ◽  
Approach To Equilibrium ◽  
The Boltzmann Equation ◽  
H Theorem ◽  
Irreversible Evolution

Like most of the greatest equations in science, the Boltzmann equation is not only beautiful but also generous. Indeed, it delivers a great deal of information without imposing a detailed knowledge of its solutions. In fact, Boltzmann himself derived most if not all of his main results without ever showing that his equation did admit rigorous solutions. This Chapter illustrates one of the most profound contributions of Boltzmann, namely the famous H-theorem, providing the first quantitative bridge between the irreversible evolution of the macroscopic world and the reversible laws of the underlying microdynamics.

Boltzmann’s Kinetic Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Statistical Physics ◽  
Neutron Transport ◽  
Condensed Matter ◽  
Relativistic Fluids ◽  
Classical Statistical Mechanics ◽  
Dilute Gas ◽  
Equilibrium Processes ◽  
The Boltzmann Equation

Kinetic theory is the branch of statistical physics dealing with the dynamics of non-equilibrium processes and their relaxation to thermodynamic equilibrium. Established by Ludwig Boltzmann (1844–1906) in 1872, his eponymous equation stands as its mathematical cornerstone. Originally developed in the framework of dilute gas systems, the Boltzmann equation has spread its wings across many areas of modern statistical physics, including electron transport in semiconductors, neutron transport, quantum-relativistic fluids in condensed matter and even subnuclear plasmas. In this Chapter, a basic introduction to the Boltzmann equation in the context of classical statistical mechanics shall be provided.

scholarly journals SLAVNOV–TAYLOR IDENTITY FOR NONEQUILIBRIUM QUARK–GLUON PLASMA

2001 ◽  
Vol 16 (08) ◽  
pp. 531-540 ◽  
Author(s):  
K. OKANO
Keyword(s):  
Quark Gluon Plasma ◽  
Gluon Plasma ◽  
Polarization Tensor ◽  
Gluon Polarization ◽  
Time Path

Within the closed-time-path formalism of nonequilibrium QCD, we derive a Slavnov–Taylor (ST) identity for the gluon polarization tensor. The ST identity takes the same form in both Coulomb and covariant gauges. Application to quasi-uniform quark–gluon plasma (QGP) near equilibrium or nonequilibrium quasistationary QGP is made.

scholarly journals Quark Cluster Expansion Model for Interpreting Finite-T Lattice QCD Thermodynamics

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 514
Author(s):  
David Blaschke ◽  
Kirill A. Devyatyarov ◽  
Olaf Kaczmarek
Keyword(s):  
Lattice Qcd ◽  
Cluster Expansion ◽  
Quark Gluon Plasma ◽  
Degrees Of Freedom ◽  
Gluon Plasma ◽  
Polyakov Loop ◽  
Unified Approach ◽  
Narrow Temperature Interval ◽  
Levinson Theorem ◽  
Expansion Model

In this work, we present a unified approach to the thermodynamics of hadron–quark–gluon matter at finite temperatures on the basis of a quark cluster expansion in the form of a generalized Beth–Uhlenbeck approach with a generic ansatz for the hadronic phase shifts that fulfills the Levinson theorem. The change in the composition of the system from a hadron resonance gas to a quark–gluon plasma takes place in the narrow temperature interval of 150–190 MeV, where the Mott dissociation of hadrons is triggered by the dropping quark mass as a result of the restoration of chiral symmetry. The deconfinement of quark and gluon degrees of freedom is regulated by the Polyakov loop variable that signals the breaking of the Z(3) center symmetry of the color SU(3) group of QCD. We suggest a Polyakov-loop quark–gluon plasma model with O(αs) virial correction and solve the stationarity condition of the thermodynamic potential (gap equation) for the Polyakov loop. The resulting pressure is in excellent agreement with lattice QCD simulations up to high temperatures.

scholarly journals Medium induced QCD cascades: broadening and rescattering during branching

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
E. Blanco ◽  
K. Kutak ◽  
W. Płaczek ◽  
M. Rohrmoser ◽  
R. Straka
Keyword(s):  
Momentum Transfer ◽  
Quark Gluon Plasma ◽  
Evolution Equations ◽  
Gaussian Approximation ◽  
Gluon Plasma ◽  
Jet Quenching ◽  
Diffusive Approximation

Abstract We study evolution equations describing jet propagation through quark-gluon plasma (QGP). In particular we investigate the contribution of momentum transfer during branching and find that such a contribution is sizeable. Furthermore, we study various approximations, such as the Gaussian approximation and the diffusive approximation to the jet-broadening term. We notice that in order to reproduce the BDIM equation (without the momentum transfer in the branching) the diffusive approximation requires a very large value of the jet-quenching parameter $$ \hat{q} $$ q ̂ .

Sign in / Sign up

Export Citation Format

Share Document