Effect of Hot Baryons on the Weak-Lensing Shear Power Spectrum

We investigate the impact of the intracluster medium on the weak-lensing shear power spectrum (PS). Using a halo model we find that, compared to the dark matter only case, baryonic pressure leads to a suppression of the shear PS on the order of a few percent or more for $l \gtrsim 1000$. Cooling/cooled baryons and the intergalactic medium can further alter the shear PS. Therefore, the interpretation of future precision weak lensing data at high multipoles must take into account the effects of baryons.Comment: 4 pages, 3 figure

Formalization of the fundamental group in untyped set theory using auto2

We present a new framework for formalizing mathematics in untyped set theory using auto2. Using this framework, we formalize in Isabelle/FOL the entire chain of development from the axioms of set theory to the definition of the fundamental group for an arbitrary topological space. The auto2 prover is used as the sole automation tool, and enables succinct proof scripts throughout the project.Comment: 17 pages, accepted for ITP 201

Equivalence of Two Approaches for Quantum-Classical Hybrid Systems

We discuss two approaches that are used frequently to describe quantum-classical hybrid system. One is the well-known mean-field theory and the other adopts a set of hybrid brackets which is a mixture of quantum commutators and classical Poisson brackets. We prove that these two approaches are equivalent.Comment: 9 page