562 research outputs found
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
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