Magnetic Fields In Relativistic Collisionless Shocks

We present a systematic study on magnetic fields in Gamma-Ray Burst (GRB) external forward shocks (FSs). There are 60 (35) GRBs in our X-ray (optical) sample, mostly from Swift. We use two methods to study epsilon_B (fraction of energy in magnetic field in the FS). 1. For the X-ray sample, we use the constraint that the observed flux at the end of the steep decline is $\ge$ the X-ray FS flux. 2. For the optical sample, we use the condition that the observed flux arises from the FS (optical sample light curves decline as ~t^-1, as expected for the FS). Making a reasonable assumption on E (jet isotropic equivalent kinetic energy), we converted these conditions into an upper limit (measurement) on epsilon_B n^{2/(p+1)} for our X-ray (optical) sample, where n is the circumburst density and p is the electron index. Taking n=1 cm^-3, the distribution of epsilon_B measurements (upper limits) for our optical (X-ray) sample has a range of ~10^-8 -10^-3 (~10^-6 -10^-3) and median of ~few x 10^-5 (~few x 10^-5). To characterize how much amplification is needed, beyond shock compression of a seed magnetic field ~10 muG, we expressed our results in terms of an amplification factor, AF, which is very weakly dependent on n (AF propto n^0.21 ). The range of AF measurements (upper limits) for our optical (X-ray) sample is ~ 1-1000 (~10-300) with a median of ~50 (~50). These results suggest that some amplification, in addition to shock compression, is needed to explain the afterglow observations.Comment: Accepted to ApJ. Minor changes after Referee Report. 22 Pages, 7 Figure

Exceptional zero formulae and a conjecture of Perrin-Riou

Let $A/\mathbb{Q}$ be an elliptic curve with split multiplicative reduction at a prime $p$. We prove (an analogue of) a conjecture of Perrin-Riou, relating $p$-adic Beilinson$-$Kato elements to Heegner points in $A(\mathbb{Q})$, and a large part of the rank-one case of the Mazur$-$Tate$-$Teitelbaum exceptional zero conjecture for the cyclotomic $p$-adic $L$-function of $A$. More generally, let $f$ be the weight-two newform associated with $A$, let $f_{\infty}$ be the Hida family of $f$, and let $L_{p}(f_{\infty},k,s)$ be the Mazur$-$Kitagawa two-variable $p$-adic $L$-function attached to $f_{\infty}$. We prove a $p$-adic Gross$-$Zagier formula, expressing the quadratic term of the Taylor expansion of $L_{p}(f_{\infty},k,s)$ at $(k,s)=(2,1)$ as a non-zero rational multiple of the extended height-weight of a Heegner point in $A(\mathbb{Q})$

The Return of the Native: the indigenous challenge in Latin America

In this paper Rodolfo Stavenhagen explores the evolution of indigenous movements in Latin America. Indigenous organisations have sprung up in their thousands since the 1960s and have become a new and formidable force for social and political change. Stavenhagen describes the factors which account for the rise of awareness within indigenous communities, such as disillusionment with the land reform and populist indigenista policies. He goes on to discuss the way in which small, grassroots organisations, concerned largely with specific socio-economic issues, have developed into large, country-wide coalitions calling for autonomy and self-determination. Although these movements have no universal ideology as such, Stavenhagen argues that the discourse created has changed both indigenous peoples' self-perception and the way in which they are viewed by the political elite both at home and abroad. Moreover, this, in time, and in tandem with the important constitutional and legislative changes already achieved, should encourage the intercultural mestizaje which he sees as the only means by which Indians and Ladinos can live on equal terms

Time as a statistical variable and intrinsic decoherence

We propose a novel approach to intrinsic decoherence without adding new assumptions to standard quantum mechanics. We generalize the Liouville equation just by requiring the dynamical semigroup property of time evolution and dropping the unitarity requirement. With no approximations and statistical assumptions we find a generalized Liouville equation which depends on two characteristic time t1 and t2 and reduces to the usual equation in the limit t1 = t2 -> 0. However, for t1 and t2 arbitrarily small but finite, our equation can be written as a finite difference equation which predicts state reduction to the diagonal form in the energy representation. The rate of decoherence becomes faster at the macroscopic limit as the energy scale of the system increases. In our approach the evolution time appears, a posteriori, as a statistical variable with a Poisson-gamma function probability distribution as if time evolution would take place randomly at average intervals t2 each evolution having a time width t1. This view point is supported by the derivation of a generalized Tam Mandelstam inequality. The relation with previous work by Milburn, with laser and micromaser theory and many experimental testable examples are described.Comment: 24 pages, e-mail: [email protected]. revised versio