4,408 research outputs found
Positivity of heights of codimension 2 cycles over function field of characteristic 0
In this note, we show how the classical Hodge index theorem implies the Hodge
index conjecture of Beilinson for height pairing of homologically trivial
codimension two cycles over function field of characteristic 0. Such an index
conjecture has been used in our paper on Gross-Schoen cycles to deduce the
Bogomolov conjecture and a lower bound for Hodge class (or Faltings height)
from some conjectures about metrized graphs which have just been recently
proved by Zubeyir Cinkir
Construction of the Symbol Invariant of Partition
Symbol is used to describe the Springer correspondence for the classical
groups. We prove two structure theorems of symbol. We propose a construction of
the symbol of the rigid partitions in the , , and theories.
This construction is natural and consists of two basic building blocks. Using
this construction, we give closed formulas of symbols for the rigid partitions
in the , and theories. One part of the closed formula is
universal and other parts are determined by the specific theory. A comparison
of between this closed formula and the old one is made. Previous results can be
illustrated more clearly by this closed formula.Comment: 27 page
Fingerprint Invariant of Partitions and Construction
The fingerprint invariant of partitions can be used to describe the
Kazhdan-Lusztig map for the classical groups. We discuss the basic properties
of fingerprint. We construct the fingerprints of rigid partitions in the ,
, and theories. To calculate the fingerprint of a rigid semisimple
operator , we decompose
into several blocks. We define operators to calculate the fingerprint for each
block using the results of fingerprint of the unipotent operators.Comment: 23 pages,30 figure
Invariants of partitions and representative elements
The symbol invariant is used to describe the Springer correspondence for the
classical groups by Lusztig. And the fingerprint invariant can be used to
describe the Kazhdan-Lusztig map. They are invariants of rigid semisimple
operators described by pairs of partitions . We
construct a nice representative element of the rigid semisimple operators with
the same symbol invariant. The fingerprint of the representative element can be
obtained immediately. We also discuss the representative element of rigid
semisimple operator with the same fingerprint invariant. Our construction can
be regarded as the maps between these two invariants.Comment: 12 pages, 15 figures. arXiv admin note: text overlap with
arXiv:1711.0344
On the Averaged Colmez Conjecture
The Colmez conjecture, proposed by Colmez, is a conjecture expressing the
Faltings height of a CM abelian variety in terms of some linear combination of
logarithmic derivatives of Artin L-functions. The aim of this paper to prove an
averaged version of the conjecture
Neutral Higgs production on LHC in the two-Higgs-doublet model with spontaneous violation
Spontaneous CP violation motivates the introduction of two Higgs doublets in
the electroweak theory, such a simple extension of the standard model has five
physical Higgs bosons and rich CP-violating sources. Exploration on more than
one Higgs boson is a direct evidence for new physics beyond the standard model.
The neutral Higgs production at LHC is investigated in such a general two Higgs
doublet model with spontaneous CP violation, it is shown that the production
cross section and decays of the neutral Higgs boson can significantly be
different from the predictions from the standard model.Comment: 15 pages, 12 figures, published version in PR
Large phase shift of (1+1)-dimensional nonlocal spatial solitons in lead glass
The large phase shift of strongly nonlocal spatial optical soliton(SNSOS) in
the (1+1)-dimensional [(1+1)D] lead glass is investigated using the
perturbation method. The fundamental soliton solution of the nonlocal nonlinear
Schodinger equation(NNLSE) under the second approximation in strongly nonlocal
case is obtained. It is found that the phase shift rate along the propagation
direction of such soliton is proportional to the degree of nonlocality, which
indicates that one can realize Pi-phase-shift within one Rayleigh distance in
(1+1)D lead glass. A full comprehension of the nonlocality-enhancement to the
phase shift rate of SNSOS is reached via quantitative comparisons of phase
shift rates in different nonlocal systems
Fast generations of tree-type three-dimensional entanglement via Lewis-Riesenfeld invariants and transitionless quantum driving
Recently, a novel three-dimensional entangled state called tree-type
entanglement, which is likely to have applications for improving quantum
communication security, was prepared via adiabatic passage by Song et al.
[Phys. Rev. A 93, 062321 (2016)]. Here we propose two schemes for fast
generations of tree-type three-dimensional entanglement among three spatially
separated atoms via shortcuts to adiabatic passage. With the help of quantum
Zeno dynamics, two kinds of different but equivalent methods, Lewis-Riesenfeld
invariants and transitionless quantum driving, are applied to construct
shortcuts to adiabatic passage. The comparisons between the two methods are
discussed. The strict numerical simulations show that the tree-type
three-dimensional entangled states can be fast prepared with quite high
fidelities and the two schemes are both robust against the variations in the
parameters, atomic spontaneous emissions and the cavity-fiber photon leakages.Comment: arXiv admin note: text overlap with arXiv:1605.0622
Fast adiabatic quantum state transfer and entanglement generation between two atoms via dressed states
Recently, a new method, which can significantly speed up adiabatic quantum
state transfer by using dressed states, was proposed by Baksic \emph{et~al.}
[Phys. Rev. Lett. \textbf{116}, 230503 (2016)]. Assisted by quantum Zeno
dynamics, we develop this dressed-state method to achieve shortcuts to complete
and fractional stimulated Raman adiabatic passage for speeding up adiabatic
two-atom quantum state transfer and maximum entanglement generation,
respectively. By means of some numerical simulations, we determine the
parameters used in the scheme which can guarantee the feasibility and
efficiency both in theory and experiment. Besides, we give strict numerical
simulations to discuss the scheme's robustness, and the results show the scheme
is robust against the variations in the parameters, atomic spontaneous
emissions and the photon leakages from the cavity
Exact SO(5) Symmetry in spin 3/2 fermionic system
The spin 3/2 fermion models with contact interactions have a {\it generic}
SO(5) symmetry without any fine-tuning of parameters. Its physical consequences
are discussed in both the continuum and lattice models. A Monte-Carlo algorithm
free of the sign problem at any doping and lattice topology is designed when
the singlet and quintet interactions satisfy , thus making it possible to study different competing orders with
high numerical accuracy. This model can be accurately realized in ultra-cold
atomic systems.Comment: 5 pages, 1 figs, more references adde
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