On Two Kinds of Differential Operators on General Smooth Surfaces

Two kinds of differential operators that can be generally defined on an arbitrary smooth surface in a finite dimensional Euclid space are studied, one is termed as surface gradient and the other one as Levi-Civita gradient. The surface gradient operator is originated from the differentiability of a tensor field defined on the surface. Some integral and differential identities have been theoretically studied that play the important role in the studies on continuous mediums whose geometrical configurations can be taken as surfaces and on interactions between fluids and deformable boundaries. The definition of Levi-Civita gradient is based on Levi-Civita connections generally defined on Riemann manifolds. It can be used to set up some differential identities in the intrinsic/coordiantes-independent form that play the essential role in the theory of vorticity dynamics for two dimensional flows on general fixed smooth surfaces

On the Ground State Wave Function of Matrix Theory

We propose an explicit construction of the leading terms in the asymptotic expansion of the ground state wave function of BFSS SU(N) matrix quantum mechanics. Our proposal is consistent with the expected factorization property in various limits of the Coulomb branch, and involves a different scaling behavior from previous suggestions. We comment on some possible physical implications.Comment: 21 page

Spin-polarized currents generated by magnetic Fe atomic chains

Fe-based devices are widely used in spintronics because of high spin-polarization and magnetism. In this work, free-standing Fe atomic chains were proposed to be used as the thinnest wires to generate spin-polarized currents due to the spin-polarized energy bands. By ab initio calculations, the zigzag structure was found more stable than the wide-angle zigzag structure and has higher ratio of spin-up and spin-down currents. By our theoretical prediction, Fe atomic chains have sufficiently long thermal lifetime only at T<=150 K, while C atomic chains are very stable even at T=1000 K. This result means that the spintronic devices based on Fe chains could only work at low temperature. A system constructed by a short Fe chain sandwiched between two graphene electrodes was proposed as a spin-polarized current generator, while a C chain does not have such property. The present work may be instructive and meaningful to further practical applications based on recent technical development on the preparation of metal atomic chains [Proc. Natl. Acad. Sci. U.S.A. 107, 9055 (2010)].Comment: Nanotechnology (2014