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 $B_n$, $C_n$, and $D_n$ 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 $B_n, C_n$, and $D_n$ 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 $B_n$, $C_n$, and $D_n$ theories. To calculate the fingerprint of a rigid semisimple operator $(\lambda^{'};\lambda^{"})$, we decompose $\lambda^{'}+\lambda^{"}$ 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 $(\lambda^{'}, \lambda^{"})$. 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 CPCP 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 $U_0\le U_2\le -{3\over5} U_0 (U_0\le 0)$, 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