Heisenberg equation for a nonrelativistic particle on a hypersurface: from the centripetal force to a curvature induced force

In classical mechanics, a nonrelativistic particle constrained on an $N-1$ curved hypersurface embedded in $N$ flat space experiences the centripetal force only. In quantum mechanics, the situation is totally different for the presence of the geometric potential. We demonstrate that the motion of the quantum particle is "driven" by not only the the centripetal force, but also a curvature induced force proportional to the Laplacian of the mean curvature, which is fundamental in the interface physics, causing curvature driven interface evolution.Comment: 4 page

The centripetal force law and the equation of motion for a particle on a curved hypersurface

It is pointed out that the current form of extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version for it is established without regard to the fact that the particle can never depart from the geodesics on the surface. Once the fact be taken into consideration, the equation takes that same form as that for centripetal force law, provided that the symbols are re-interpreted so that the law is applicable for higher dimensions. The controversial issue of constructing operator forms of these equations is addressed, and our studies show the quantization of constrained system based on the extrinsic equation of motion is favorable.Comment: 5 pages, major revisio

On Asynchronous Session Semantics

This paper studies a behavioural theory of the π-calculus with session types under the fundamental principles of the practice of distributed computing — asynchronous communication which is order-preserving inside each connection (session), augmented with asynchronous inspection of events (message arrivals). A new theory of bisimulations is introduced, distinct from either standard asynchronous or synchronous bisimilarity, accurately capturing the semantic nature of session-based asynchronously communicating processes augmented with event primitives. The bisimilarity coincides with the reduction-closed barbed congruence. We examine its properties and compare them with existing semantics. Using the behavioural theory, we verify that the program transformation of multithreaded into event-driven session based processes, using Lauer-Needham duality, is type and semantic preserving

A Survey for Low-Mass Stars and Brown Dwarfs in the Eta Cha and Eps Cha Young Associations

I present the results of a search for new low-mass stars and brown dwarfs in the Eta Cha and Eps Cha young associations. Within radii of 1.5 and 0.5 deg surrounding Eta Cha and Eps Cha, respectively, I have constructed color-magnitude diagrams from DENIS and 2MASS photometry and have obtained spectra of the candidate low-mass members therein. The five candidates in Eta Cha are classified as four field M dwarfs and one carbon star. No new members are found in this survey, which is complete for M_sun=0.015-0.15 according to the evolutionary models of Chabrier and Baraffe. Thus, an extended population of low-mass members is not present in Eta Cha out to four times the radius of the known membership. Meanwhile, the three candidate members of Eps Cha are classified as young stars, and thus likely members of the association, based on Li absorption and gravity-sensitive absorption lines. These new sources have spectral types of M2.25, M3.75, and M5.75, corresponding to masses of 0.45, 0.25, and 0.09 M_sun by the models of Chabrier and Baraffe. For one of these stars, intense H(alpha) emission, forbidden line emission, and strong K-band excess emission suggest the presence of accretion, an outflow, and a disk, respectively. This young star is also much fainter than expected for an association member at its spectral type, which could indicate that it is seen in scattered light. No brown dwarfs are detected in Eps Cha down to the completeness limit of 0.015 M_sun. The absence of brown dwarfs in these associations is statistically consistent with the mass functions measured in star-forming regions, which exhibit only ~2 and ~1 brown dwarfs for stellar samples at the sizes of the Eta Cha and Eps Cha associations.Comment: 19 pages, The Astrophysical Journal, 2004, v616 (December 1