Fixed points and flow analysis on off-equilibrium dynamics in the boson Boltzmann equation

We consider fixed points of steady solutions and flow directions using the boson Boltzmann equation that is a one-dimensionally reduced kinetic equation after the angular integration. With an elastic collision integral of the two-to-two scattering process, in the dense (dilute) regime where the dist...

Full description

Saved in:
Bibliographic Details
Published inAnnals of physics Vol. 386; pp. 76 - 96
Main Authors Fukushima, Kenji, Murase, Koichi, Pu, Shi
Format Journal Article
LanguageEnglish
Published United States Elsevier Inc 01.11.2017
Subjects
BOLTZMANN EQUATION
BOSONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COLLISION INTEGRALS
DISTRIBUTION FUNCTIONS
MATHEMATICAL SOLUTIONS
Online AccessGet full text

Cover

More Information
Summary:We consider fixed points of steady solutions and flow directions using the boson Boltzmann equation that is a one-dimensionally reduced kinetic equation after the angular integration. With an elastic collision integral of the two-to-two scattering process, in the dense (dilute) regime where the distribution function is large (small), the boson Boltzmann equation has approximate fixed points with a power-law spectrum in addition to the thermal distribution function. We argue that the power-law fixed point can be exact in special cases. We elaborate a graphical presentation to display evolving flow directions similarly to the renormalization group flow, which explicitly exhibits how fixed points are connected and parameter space is separated by critical lines. We discuss that such a flow diagram contains useful information on thermalization processes out of equilibrium.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2017.08.032