5,283 research outputs found
On the K-power free number sequence
The main purpose of this paper is to study the distribution properties of the k-power free numbers, and give an interesting asymptotic formula for it
On the uniqueness of the foliation of spheres of constant mean curvature in asymptotically flat 3-manifolds
In this note we study constant mean curvature surfaces in asymptotically flat
3-manifolds. We prove that, in an asymptotically flat 3-manifold with positive
mass, stable spheres of given constant mean curvature outside a fixed compact
subset are unique. Therefore we are able to conclude that there is a unique
foliation of stable spheres of constant mean curvature in an asymptotically
flat 3-manifold with positive mass.Comment: 22 page
Local Entanglement and quantum phase transition in spin models
Due to the phase interference of electromagnetic wave, one can recover the
total image of one object from a small piece of holograph, which records the
interference pattern of two laser light reflected from it. Similarly, the
quantum superposition principle allows us to derive the global phase diagram of
quantum spin models by investigating a proper local measurement. In the present
paper, we study the two-site entanglement in the antifferomagnetic spin models
with both spin-1/2 and 1. We show that its behaviors reveal some important
information on the global properties and the quantum phase transition of these
systems.Comment: 6 pages, 7 figure
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