5 research outputs found
Typicality versus thermality: An analytic distinction
In systems with a large degeneracy of states such as black holes, one expects
that the average value of probe correlation functions will be well approximated
by the thermal ensemble. To understand how correlation functions in individual
microstates differ from the canonical ensemble average and from each other, we
study the variances in correlators. Using general statistical considerations,
we show that the variance between microstates will be exponentially suppressed
in the entropy. However, by exploiting the analytic properties of correlation
functions we argue that these variances are amplified in imaginary time,
thereby distinguishing pure states from the thermal density matrix. We
demonstrate our general results in specific examples and argue that our results
apply to the microstates of black holes.Comment: 22 pages + appendices, 3 eps figure
Towards Jetography
As the LHC prepares to start taking data, this review is intended to provide
a QCD theorist's understanding and views on jet finding at hadron colliders,
including recent developments. My hope is that it will serve both as a primer
for the newcomer to jets and as a quick reference for those with some
experience of the subject. It is devoted to the questions of how one defines
jets, how jets relate to partons, and to the emerging subject of how best to
use jets at the LHC.Comment: 95 pages, 28 figures, an extended version of lectures given at the
CTEQ/MCNET school, Debrecen, Hungary, August 2008; v2 includes additional
discussion in several places, as well as other clarifications and additional
references
The two-body problem of a pseudo-rigid body and a rigid sphere
In this paper we consider the two-body problem of a spherical pseudo-rigid body and a rigid sphere. Due to the rotational and “re-labelling” symmetries, the system is shown to possess conservation of angular momentum and circulation. We follow a reduction procedure similar to that undertaken in the study of the two-body problem of a rigid body and a sphere so that the computed reduced non-canonical Hamiltonian takes a similar form. We then consider relative equilibria and show that the notions of locally central and planar equilibria coincide. Finally, we show that Riemann’s theorem on pseudo-rigid bodies has an extension to this system for planar relative equilibria