11,902 research outputs found
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
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