7,827 research outputs found
Crystalline Hodge cycles and Shimura curves in positive characteristics
In this paper, we seek an appropriate definition for a Shimura curve of Hodge
type in positive characteristics, i.e. a characterization of curves in positive
characteristics which are reduction of Shimura curve over the complex field.
Specifically, we study the liftablity of a curve in moduli space of principally
polarized abelian fourfolds over k, char k=p. We show that some conditions on
the crystalline Hodge cycles over such a curve imply that this curve can be
lifted to a Shimura curve.Comment: 21 pages. Comments welcom
l-adic Monodromy and Shimura curves in positive characteristics
In this paper, we seek an appropriate definition for a Shimura curve of Hodge
type in positive characteristics, i.e. a characterization, in terms of geometry
mod p, of curves in positive characteristics which are reduction of Shimura
curves over the complex field. Specifically, we study the liftablity of a curve
in moduli space of principally polarized abelian varieties over k, char k=p. We
show that some conditions on the l-adic monodromy over such a curve imply that
this curve can be lifted to a Shimura curve.Comment: 8 pages. Comments are welcome
Tensor decomposition of isocrystals characterizes Mumford curves
We seek an appropriate definition for a Shimura curve of Hodge type in
positive characteristics via characterizing curves in positive characteristics
which are reduction of Shimura curve over . In this paper, we study
the liftablity of a curve in the moduli space of principally polarized abelian
varieties over . We show that in the generic ordinary case,
some tensor decomposition of the isocrystal associated to the family imply that
this curve can be lifted to a Shimura curve.Comment: 17 pages. Comments are welcom
On Rigidity of hypersurfaces with constant curvature functions in warped product manifolds
In this paper, we first investigate several rigidity problems for
hypersurfaces in the warped product manifolds with constant linear combinations
of higher order mean curvatures as well as "weighted'' mean curvatures, which
extend the work \cite{Mon, Brendle,BE} considering constant mean curvature
functions. Secondly, we obtain the rigidity results for hypersurfaces in the
space forms with constant linear combinations of intrinsic Gauss-Bonnet
curvatures . To achieve this, we develop some new kind of Newton-Maclaurin
type inequalities on which may have independent interest.Comment: 24 pages, Ann. Glob. Anal. Geom. to appea
Annealed asymptotics for Brownian motion of renormalized potential in mobile random medium
Motivated by the study of the directed polymer model with mobile Poissonian
traps or catalysts and the stochastic parabolic Anderson model with time
dependent potential, we investigate the asymptotic behavior of
where is a constant, is the renormalized
Poisson potential of the form
and is the measure-valued process consisting of independent Brownian
particles whose initial positions form a Poisson random measure on
with Lebesgue measure as its intensity. Different scaling limits
are obtained according to the parameter and dimension . For the
logarithm of the negative exponential moment, the range of is
divided into 5 regions with various scaling rates of the orders ,
, , and , respectively. For the positive
exponential moment, the limiting behavior is studied according to the
parameters and in three regions. In the sub-critical region (),
the double logarithm of the exponential moment has a rate of . In the
critical region (), it has different behavior over two parts decided
according to the comparison of with the best constant in the Hardy
inequality. In the super-critical region ,
the exponential moments become infinite for all .Comment: 43 page
Quantum speed limits for Bell-diagonal states
Bounds of the minimum evolution time between two distinguishable states of a
system can help to assess the maximal speed of quantum computers and
communication channels. We study the quantum speed limit time of a composite
quantum states in the presence of nondissipative decoherence. For the initial
states with maximally mixed marginals, we obtain the exactly expressions of
quantum speed limit time which mainly depend on the parameters of the initial
states and the decoherence channels. Furthermore, by calculating quantum speed
limit time for the time-dependent states started from a class of initial
states, we discover that the quantum speed limit time gradually decreases in
time, and the decay rate of the quantum speed limit time would show a sudden
change at a certain critical time. Interestingly, at the same critical time,
the composite system dynamics would exhibit a sudden transition from classical
to quantum decoherence.Comment: 5 pages, 2 figure
Enhancing entanglement trapping by weak measurement and quantum measurement reversal
In this paper, we propose a scheme to enhance trapping of entanglement of two
qubits in the environment of a photonic band gap material. Our entanglement
trapping promotion scheme makes use of combined weak measurements and quantum
measurement reversals. The optimal promotion of entanglement trapping can be
acquired with a reasonable finite success probability by adjusting measurement
strengths.Comment: welcome to commen
One-step implementation of the Fredkin gate via quantum Zeno dynamics
We study one-step implementation of the Fredkin gate in a bi-modal cavity
under both resonant and large detuning conditions based on quantum Zeno
dynamics, which reduces the complexity of experiment operations. The influence
of cavity decay and atomic spontaneous emission is discussed by numerical
calculation. The results demonstrate that the fidelity and the success
probability are robust against cavity decay in both models and they are also
insensitive to atomic spontaneous emission in the large detuning model. In
addition, the interaction time is rather short in the resonant model compared
to the large detuning model.Comment: 22 pages, 7 figure
On the deformation of a Barsotti-Tate group over a curve
In this paper, we study deformations of pairs (C,G) where G is a height 2
BT(or BT_n) group over a complete curve on algebraically closed field k of
characteristic p. We prove that, if the curve C is a versal deformation of G,
then there exists a unique lifting of the pair to the Witt ring W. We apply
this result in the case of Shimura curves to obtain a lifting criterion.Comment: 20 pages, no figures. Comments welcom
Role of initial system-bath correlation on coherence trapping
We study the coherence trapping of a qubit correlated initially with a
non-Markovian bath in a pure dephasing channel. By considering the initial
qubit-bath correlation and the bath spectral density, we find that the initial
qubit-bath correlation can lead to a more efficient coherence trapping than
that of the initially separable qubit-bath state. The stationary coherence in
the long time limit can be maximized by optimizing the parameters of the
initially correlated qubit-bath state and the bath spectral density. In
addition, the effects of this initial correlation on the maximal evolution
speed for the qubit trapped to its stationary coherence state are also
explored.Comment: 5 pages,3 figures, welcome to commen
- …