26,283 research outputs found
Can an observer really catch up with light
Given a null geodesic with a point in
conjugate to along , there will be a variation of
which will give a time-like curve from to . 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
The K\"ahler-Ricci flow on surfaces of positive Kodaira dimension
The existence of K\"ahler-Einstein metrics on a compact K\"ahler manifold has
been the subject of intensive study over the last few decades, following Yau's
solution to Calabi's conjecture. The Ricci flow, introduced by Richard Hamilton
has become one of the most powerful tools in geometric analysis.
We study the K\"ahler-Ricci flow on minimal surfaces of Kodaira dimension one
and show that the flow collapses and converges to a unique canonical metric on
its canonical model. Such a canonical is a generalized K\"ahler-Einstein
metric. Combining the results of Cao, Tsuji, Tian and Zhang, we give a metric
classification for K\"aher surfaces with a numerical effective canonical line
bundle by the K\"ahler-Ricci flow. In general, we propose a program of finding
canonical metrics on canonical models of projective varieties of positive
Kodaira dimension
A compactness theorem for complete Ricci shrinkers
We prove precompactness in an orbifold Cheeger-Gromov sense of complete
gradient Ricci shrinkers with a lower bound on their entropy and a local
integral Riemann bound. We do not need any pointwise curvature assumptions,
volume or diameter bounds. In dimension four, under a technical assumption, we
can replace the local integral Riemann bound by an upper bound for the Euler
characteristic. The proof relies on a Gauss-Bonnet with cutoff argument.Comment: 28 pages, final version, to appear in GAF
Log canonical thresholds of Del Pezzo Surfaces in characteristic p
The global log canonical threshold of each non-singular complex del Pezzo
surface was computed by Cheltsov. The proof used Koll\'ar-Shokurov's
connectedness principle and other results relying on vanishing theorems of
Kodaira type, not known to be true in finite characteristic.
We compute the global log canonical threshold of non-singular del Pezzo
surfaces over an algebraically closed field. We give algebraic proofs of
results previously known only in characteristic . Instead of using of the
connectedness principle we introduce a new technique based on a classification
of curves of low degree. As an application we conclude that non-singular del
Pezzo surfaces in finite characteristic of degree lower or equal than are
K-semistable.Comment: 21 pages. Thorough rewrite following referee's suggestions. To be
published in Manuscripta Mathematic
Effect of oxygen plasma etching on graphene studied with Raman spectroscopy and electronic transport
We report a study of graphene and graphene field effect devices after
exposure to a series of short pulses of oxygen plasma. We present data from
Raman spectroscopy, back-gated field-effect and magneto-transport measurements.
The intensity ratio between Raman "D" and "G" peaks, I(D)/I(G) (commonly used
to characterize disorder in graphene) is observed to increase approximately
linearly with the number (N(e)) of plasma etching pulses initially, but then
decreases at higher Ne. We also discuss implications of our data for extracting
graphene crystalline domain sizes from I(D)/I(G). At the highest Ne measured,
the "2D" peak is found to be nearly suppressed while the "D" peak is still
prominent. Electronic transport measurements in plasma-etched graphene show an
up-shifting of the Dirac point, indicating hole doping. We also characterize
mobility, quantum Hall states, weak localization and various scattering lengths
in a moderately etched sample. Our findings are valuable for understanding the
effects of plasma etching on graphene and the physics of disordered graphene
through artificially generated defects.Comment: 10 pages, 5 figure
Flat bidifferential ideals and semihamiltonian PDEs
In this paper we consider a class of semihamiltonian systems characterized by
the existence of a special conservation law.
The density and the current of this conservation law satisfy a second order
system of PDEs which has a natural interpretation in the theory of flat
bifferential ideals. The class of systems we consider contains important
well-known examples of semihamiltonian systems. Other examples, like genus 1
Whitham modulation equations for KdV, are related to this class by a
reciprocal trasformation.Comment: 18 pages. v5: formula (36) corrected; minor change
Local trace formulae and scaling asymptotics in Toeplitz quantization, II
In the spectral theory of positive elliptic operators, an important role is
played by certain smoothing kernels, related to the Fourier transform of the
trace of a wave operator, which may be heuristically interpreted as smoothed
spectral projectors asymptotically drifting to the right of the spectrum. In
the setting of Toeplitz quantization, we consider analogues of these, where the
wave operator is replaced by the Hardy space compression of a linearized
Hamiltonian flow, possibly composed with a family of zeroth order Toeplitz
operators. We study the local asymptotics of these smoothing kernels, and
specifically how they concentrate on the fixed loci of the linearized dynamics.Comment: Typos corrected. Slight expository change
Ehrenfest time in the weak dynamical localization
The quantum kicked rotor (QKR) is known to exhibit dynamical localization in
the space of its angular momentum. The present paper is devoted to the
systematic first--principal (without a regularizer) diagrammatic calculations
of the weak--localization corrections for QKR. Our particular emphasis is on
the Ehrenfest time regime -- the phenomena characteristic for the
classical--to--quantum crossover of classically chaotic systems.Comment: 27 pages, 9 figure
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