The Formation of Classical Defects After a Slow Quantum Phase Transition

Classical defects (monopoles, vortices, etc.) are a characteristic consequence of many phase transitions of quantum fields. We show a model in which the onset of classical probability distributions, for the long-wavelength modes at early times, allows the identification of line-zeroes of the field with vortex separation. We obtain a refined version of Kibble's causal results for defect separation, but from a completely different approach. It is apparent that vortices are not created from thermal fluctuations in the Ginzburg regime.Comment: 10 pages, RevTex file. No figures. To appear in Phys. Lett.

Measurement of the CKM angles alpha and gamma at the BaBar experiment

We present recent measurements of the CKM angles alpha and gamma using data collected by the BaBar detector at the PEP-II asymmetric-energy e+ e- collider at the Stanford Linear Accelerator Center. In addition to constraints on alpha from the decays B0 -> pi+ pi-, B0 -> rho+ pi- and B0 -> rho+ rho-, we also report the first measurement of time-dependent CP asymmetries in the decay B0 -> a1+(1260) pi-. We present measurements of gamma in B+ -> D(*)0 K+ decays using a Dalitz analysis in the modes D^0 -> Ks pi+ pi- and D^0 -> pi+ pi- pi0.Comment: 5 pages, contributed to the Proceedings of Lake Louise Winter Institute 2007: Fundamental Interactions, Lake Louise, Alberta, Canada 19-24 Feb 200

An explicit open image theorem for products of elliptic curves

Let $K$ be a number field and $E_1, \ldots, E_n$ be elliptic curves over $K$, pairwise non-isogenous over $\overline{K}$ and without complex multiplication over $\overline{K}$. We study the image of the adelic representation of the absolute Galois group of $K$ naturally attached to $E_1 \times \cdots \times E_n$. The main result is an explicit bound for the index of this image in $\left\{ (x_1,\ldots,x_n) \in \operatorname{GL}_2(\hat{\mathbb{Z}})^n \bigm\vert \det x_i = \det x_j \;\; \forall i,j \right\}$.Comment: 18 pages. v2: improved expositio