Thermal Abundances of Heavy Particles

Matsumoto and Yoshimura [hep-ph/9910393] have argued that there are loop corrections to the number density of heavy particles (in thermal equilibrium with a gas of light particles) that are not Boltzmann suppressed by a factor of e^(-M/T) at temperatures T well below the mass M of the heavy particle. We argue, however, that their definition of the number density does not correspond to a quantity that could be measured in a realistic experiment. We consider a model where the heavy particles carry a conserved U(1) charge, and the light particles do not. The fluctuations of the net charge in a given volume then provide a measure of the total number of heavy particles in that same volume. We show that these charge fluctuations are Boltzmann suppressed (to all orders in perturbation theory). Therefore, we argue, the number density of heavy particles is also Boltzmann suppressed.Comment: 9 pages, 1 figure; minor improvements in revised versio

Cuntz-Pimsner C*-algebras associated with subshifts

By using C*-correspondences and Cuntz-Pimsner algebras, we associate to every subshift (also called a shift space) $X$ a C*-algebra $O_X$, which is a generalization of the Cuntz-Krieger algebras. We show that $O_X$ is the universal C*-algebra generated by partial isometries satisfying relations given by $X$. We also show that $O_X$ is a one-sided conjugacy invariant of $X$.Comment: 28 pages. This is a slightly updated version of a preprint from 2004. Submitted for publication. In version 2 the Introduction has been changed, two remarks (Remark 7.6 and 7.7) have been added and the list of references has been update

Complex-space singularities of 2D Euler flow in Lagrangian coordinates

We show that, for two-dimensional space-periodic incompressible flow, the solution can be evaluated numerically in Lagrangian coordinates with the same accuracy achieved in standard Eulerian spectral methods. This allows the determination of complex-space Lagrangian singularities. Lagrangian singularities are found to be closer to the real domain than Eulerian singularities and seem to correspond to fluid particles which escape to (complex) infinity by the current time. Various mathematical conjectures regarding Eulerian/Lagrangian singularities are presented.Comment: 5 pages, 2 figures, submitted to Physica

Singularities of Euler flow? Not out of the blue!

Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out some of the difficulties, we propose to tackle this issue for the class of flows having analytic initial data for which hypothetical real singularities are preceded by singularities at complex locations. We present some results concerning the nature of complex space singularities in two dimensions and propose a new strategy for the numerical investigation of blowup.(A version of the paper with higher-quality figures is available at http://www.obs-nice.fr/etc7/complex.pdf)Comment: RevTeX4, 10 pages, 9 figures. J.Stat.Phys. in press (updated version

Bose-Einstein condensation of magnons in TlCuCl3_3

A quantitative study of the field-induced magnetic ordering in TlCuCl$_3$ in terms of a Bose-Einstein condensation (BEC) of magnons is presented. It is shown that the hitherto proposed simple BEC scenario is in quantitative and qualitative disagreement with experiment. It is further shown that even very small Dzyaloshinsky-Moriya interactions or a staggered $g$ tensor component of a certain type can change the BEC picture qualitatively. Such terms lead to a nonzero condensate density for all temperatures and a gapped quasiparticle spectrum. Including this type of interaction allows us to obtain good agreement with experimental data.Comment: 2 pages, 2 figures, submitted to SCES'0

Why Two Renormalization Groups are Better than One

The advantages of using more than one renormalization group (RG) in problems with more than one important length scale are discussed. It is shown that: i) using different RG's can lead to complementary information, i.e. what is very difficult to calculate with an RG based on one flow parameter may be much more accessible using another; ii) using more than one RG requires less physical input in order to describe via RG methods the theory as a function of its parameters; iii) using more than one RG allows one to solve problems with more than one diverging length scale. The above points are illustrated concretely in the context of both particle physics and statistical physics using the techniques of environmentally friendly renormalization. Specifically, finite temperature $\lambda\phi^4$ theory, an Ising-type system in a film geometry, an Ising-type system in a transverse magnetic field, the QCD coupling constant at finite temperature and the crossover between bulk and surface critical behaviour in a semi-infinite geometry are considered.Comment: 17 pages LaTex; to be published in the Proceedings of RG '96, Dubn