5 research outputs found
Shear Viscosity of a Hot Pion Gas
The shear viscosity of an interacting pion gas is studied using the Kubo
formalism as a microscopic description of thermal systems close to global
equilibrium. We implement the skeleton expansion in order to approximate the
retarded correlator of the viscous part of the energy-momentum tensor. After
exploring this in theory we show how the skeleton expansion can be
consistently applied to pions in chiral perturbation theory. The shear
viscosity is determined by the spectral width, or equivalently, the mean
free path of pions in the heat bath. We derive a new analytical result for the
mean free path which is well-conditioned for numerical evaluation and discuss
the temperature and pion-mass dependence of the mean free path and the shear
viscosity. The ratio of the interacting pion gas exceeds the lower
bound from AdS/CFT correspondence.Comment: 12 pages, 7 figures. Revision includes additional Appendix B. Matches
published versio
Specifying Real Numbers in CASL
We present a weak theory BasicReal of the real numbers in the first order specification language Casl. The aim is to provide a datatype for practical purposes, including the central notions and results of basic analysis. BasicReal captures for instance e and ; as well as the trigonometric and other standard functions. Concepts such as continuity, differentiation and integration are shown to be definable and tractable in this setting; Newton's Method is presented as an example of a numerical application. Finally, we provide a proper connection between the specified datatype BasicReal and specifications of the real numbers in higher order logic and various set theories