Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum-classical limit

This work identifies geometric effects on dynamics due to nonadiabatic couplings in Born Oppenheimer systems and provides a systematic method for deriving corrections to mixed quantum-classical methods. Specifically, an exact path integral formulation of the quantum nonadiabatic dynamics of Born Oppenheimer systems is described. Stationary phase approximations to the propagator for full quantum dynamics are derived. It is shown that quantum corrections to mixed quantum classical methods can be obtained through stationary phase approximations to the full quantum dynamics. A rigorous description of the quantum corrections due to electronic nonadiabatic coupling on the nuclear dynamics within the Ehrenfest framework is obtained. The fewest switches surface hopping method is shown to be obtained as a quasiclassical approximation to the dynamics and natural semiclassical extensions to include classically forbidden nonadiabatic transitions are suggested.Comment: 26 pages, 2 figures. Accepted for publication, Journal of Chemical Physic

Web 2.0 and the ever elusive balance between information explosion and data mining

In a fascinating tussle of perspectives in Volume 6 and issue no 3 of april 2008 Frontiers in Ecology and Evolution, Martin A Nuñez and Gregory M Crustinger enlist ways to brace up with the recent literature. They advocate that PhD students should choose a well studied system to have better chances of success. On the other side of this fascinating tussle Daniel Simberloff and Nathan J Sanders agree with there enthusiastic case and approaches for bracing up with the recent literature. However, they disagree with the play safe strategy of start-ups in ecology and evolution.

For me this tussle of perspectives is really fascinating. It underlines the story of our times. In the times of information explosion, should we concentrate on mining this information for knowledge or should we keep adding to this information explosion. This dilemma fits well in the context of the tussle by a quote from Nassim Nicholas Taleb “ It is almost impossible these days to finish PhD without excessive intellectual curiosity and it is impossible to get a faculty position without narrowly specializing in a chosen field ”.
Here in this letter, I want to harmonize the two perspectives by arguing that coexistence of information explosion and data mining is possible. We should strive for that ever elusive balance and I discuss below how Web 2.0 will enable it. Web 2.0, still in its infancy already shows promising results and I discuss below these usages

Gersten Conjecture For Equivariant K-theory And Applications

For a reductive group scheme over a regular semi-local ring, we prove an equivarinat version of the Gersten conjecture. We draw some interesting consequences for the representation rings of such reductive group schemes. We also prove the rigidity for the equivariant K-theory of reductive group schemes over a henselian local ring. This is then used to compute the equivariant K-theory of algebraically closed fields