37,789 research outputs found

### A new model for the double well potential

A new model for the double well potential is presented in the paper. In the
new potential, the exchanging rate could be easily calculated by the
perturbation method in supersymmetric quantum mechanics. It gives good results
whether the barrier is high or sallow. The new model have many merits and may
be used in the double well problem.Comment: 3pages, 3figure

### Ricci flow on K\"ahler-Einstein manifolds

In our previous paper math.DG/0010008, we develop some new techniques in
attacking the convergence problems for the K\"ahler Ricci flow. The one of main
ideas is to find a set of new functionals on curvature tensors such that the
Ricci flow is the gradient like flow of these functionals. We successfully find
such functionals in case of Kaehler manifolds. On K\"ahler-Einstein manifold
with positive scalar curvature, if the initial metric has positive bisectional
curvature, we prove that these functionals have a uniform lower bound, via the
effective use of Tian's inequality. Consequently, we prove the following
theorem: Let $M$ be a K\"ahler-Einstein manifold with positive scalar
curvature. If the initial metric has nonnegative bisectional curvature and
positive at least at one point, then the K\"ahler Ricci flow will converge
exponentially fast to a K\"ahler-Einstein metric with constant bisectional
curvature. Such a result holds for K\"ahler-Einstein orbifolds.Comment: 49 pages. This is a revised version. Sections 4 and 5 are simplified
and streamline

### Calabi-Yau manifolds from pairs of non-compact Calabi-Yau manifolds

Most of Calabi-Yau manifolds that have been considered by physicists are
complete intersection Calabi-Yau manifolds of toric varieties or some quotients
of product types. Purpose of this paper is to introduce a different and rather
new kind of construction method of Calabi-Yau manifolds by pasting two
non-compact Calabi-Yau manifolds. We will also in some details explain a
curious and mysterious similarity with construction of some $G_2$-manifolds
(also called Joyce manifolds), which are base spaces for M-theory.Comment: 10 pages. Accepted for publication in JHE

### Can an observer really catch up with light

Given a null geodesic $\gamma_0(\lambda)$ with a point $r$ in $(p,q)$
conjugate to $p$ along $\gamma_0(\lambda)$, there will be a variation of
$\gamma_0(\lambda)$ which will give a time-like curve from $p$ to $q$. This is
a well-known theory proved in the famous book\cite{2}. In the paper we prove
that the time-like curves coming from the above-mentioned variation have a
proper acceleration which approaches infinity as the time-like curve approaches
the null geodesic. This means no observer can be infinitesimally near the light
and begin at the same point with the light and finally catch the light. Only
separated from the light path finitely, does the observer can begin at the same
point with the light and finally catch the light.Comment: 6 pages, no figures, submited to Physical Review

### Entanglement and quantum phase transitions

We examine several well known quantum spin models and categorize behavior of
pairwise entanglement at quantum phase transitions. A unified picture on the
connection between the entanglement and quantum phase transition is given.Comment: 4 pages, 3 figure

- …