Focusing of branes in warped backgrounds

Branes are embedded surfaces in a given background (bulk) spacetime. Assuming a warped bulk, we investigate, in analogy with the case for geodesics, the notion of {\em focusing} of families of such embedded, extremal 3--branes in a five dimensional background . The essential tool behind our analysis, is the well-known generalised Raychaudhuri equations for surface congruences. In particular, we find explicit solutions of these equations, which seem to show that families of 3--branes can focus along lower dimensional submanifolds depending on where the initial expansions are specified. We conclude with comments on the results obtained and possibilities about future work along similar lines.Comment: 11 pages, one figur

Classical and quantum mechanics of a particle on a rotating loop

The toy model of a particle on a vertical rotating circle in the presence of uniform gravitational/ magnetic fields is explored in detail. After an analysis of the classical mechanics of the problem we then discuss the quantum mechanics from both exact and semi--classical standpoints. Exact solutions of the Schrodinger equation are obtained in some cases by diverse methods. Instantons, bounces are constructed and semi-classical, leading order tunneling amplitudes/decay rates are written down. We also investigate qualitatively the nature of small oscillations about the kink/bounce solutions. Finally, the connections of these toy examples with field theoretic and statistical mechanical models of relevance are pointed out.Comment: 30 pages, RevTex, 7 figure