The Precise Formula in a Sine Function Form of the norm of the Amplitude and the Necessary and Sufficient Phase Condition for Any Quantum Algorithm with Arbitrary Phase Rotations

In this paper we derived the precise formula in a sine function form of the norm of the amplitude in the desired state, and by means of he precise formula we presented the necessary and sufficient phase condition for any quantum algorithm with arbitrary phase rotations. We also showed that the phase condition: identical rotation angles, is a sufficient but not a necessary phase condition.Comment: 16 pages. Modified some English sentences and some proofs. Removed a table. Corrected the formula for kol on page 10. No figure

Quantum Hall Effect in Thin Films of Three-Dimensional Topological Insulators

We show that a thin film of a three-dimensional topological insulator (3DTI) with an exchange field is a realization of the famous Haldane model for quantum Hall effect (QHE) without Landau levels. The exchange field plays the role of staggered fluxes on the honeycomb lattice, and the hybridization gap of the surface states is equivalent to alternating on-site energies on the AB sublattices. A peculiar phase diagram for the QHE is predicted in 3DTI thin films under an applied magnetic field, which is quite different from that either in traditional QHE systems or in graphene.Comment: 4 pages, 4 figure

A topological look at the quantum spin Hall state

We propose a topological understanding of the quantum spin Hall state without considering any symmetries, and it follows from the gauge invariance that either the energy gap or the spin spectrum gap needs to close on the system edges, the former scenario generally resulting in counterpropagating gapless edge states. Based upon the Kane-Mele model with a uniform exchange field and a sublattice staggered confining potential near the sample boundaries, we demonstrate the existence of such gapless edge states and their robust properties in the presence of impurities. These gapless edge states are protected by the band topology alone, rather than any symmetries.Comment: 5 pages, 4 figure

Electronic properties of bilayer phosphorene quantum dots in the presence of perpendicular electric and magnetic fields

Using the tight-binding approach, we investigate the electronic properties of bilayer phosphorene (BLP) quantum dots (QDs) in the presence of perpendicular electric and magnetic fields. Since BLP consists of two coupled phosphorene layers, it is of interest to examine the layer-dependent electronic properties of BLP QDs, such as the electronic distributions over the two layers and the so-produced layer-polarization features, and to see how these properties are affected by the magnetic field and the bias potential. We find that in the absence of a bias potential only edge states are layer-polarized while the bulk states are not, and the layer-polarization degree (LPD) of the unbiased edge states increases with increasing magnetic field. However, in the presence of a bias potential both the edge and bulk states are layer-polarized, and the LPD of the bulk (edge) states depends strongly (weakly) on the interplay of the bias potential and the interlayer coupling. At high magnetic fields, applying a bias potential renders the bulk electrons in a BLP QD to be mainly distributed over the top or bottom layer, resulting in layer-polarized bulk Landau levels (LLs). In the presence of a large bias potential that can drive a semiconductor-to-semimetal transition in BLP, these bulk LLs exhibit different magnetic-field dependences, i.e., the zeroth LLs exhibit a linear-like dependence on the magnetic field while the other LLs exhibit a square-root-like dependence.Comment: 11 pages, 6 figure

Correlations and fluctuations measured by the CMS experiment in pp and PbPb

Measurements of charged dihadron angular correlations are presented in proton-proton (pp) and Lead-Lead (PbPb) collisions, over a broad range of pseudorapidity and azimuthal angle, using the CMS detector at the LHC. In very high multiplicity pp events at center-of-mass energy of 7 TeV, a striking "ridge"-like structure emerges in the two-dimensional correlation function for particle pairs with intermediate pt of 1-3 GeVc, in the kinematic region 2.0<|\Delta\eta|<4.8 and small \Delta\phi, which is similar to observations in heavy-ion collisions. Studies of this new effect as a function of particle transverse momentum are discussed. The long-range and short-range dihadron correlations are also studied in PbPb collision at a nucleon-nucleon center-of-mass energy of 2.76 TeV, as a function of transverse momentum and collision centrality. A Fourier analysis of the long-range dihadron correlations is presented and discussed in the context of CMS measurements of higher order flow coefficients.Comment: 8 pages, 8 figures, proceedings for Quark Matter 2011, Annecy, France, May 23-28, 201

About a possible 3rd order phase transition at T=0 in 4D gluodynamics

We revisit the question of the convergence of lattice perturbation theory for a pure SU(3) lattice gauge theory in 4 dimensions. Using a series for the average plaquette up to order 10 in the weak coupling parameter beta^{-1}, we show that the analysis of the extrapolated ratio and the extrapolated slope suggests the possibility of a non-analytical power behavior of the form (1/\beta -1/5.7(1))^{1.0(1)}, in agreement with another analysis based on the same asumption. This would imply that the third derivative of the free energy density diverges near beta =5.7. We show that the peak in the third derivative of the free energy present on 4^4 lattices disappears if the size of the lattice is increased isotropically up to a 10^4 lattice. On the other hand, on 4 x L^3 lattices, a jump in the third derivative persists when L increases. Its location coincides with the onset of a non-zero average for the Polyakov loop. We show that the apparent contradiction at zero temperature can be resolved by moving the singularity in the complex 1/\beta plane. If the imaginary part of the location of the singularity Gamma is within the range 0.001< Gamma < 0.01, it is possible to limit the second derivative of P within an acceptable range without affecting drastically the behavior of the perturbative coefficients. We discuss the possibility of checking the existence of these complex singularities by using the strong coupling expansion or calculating the zeroes of the partition function.Comment: 7 pages, 9 figures, contains a resolution of the main paradox and a discussion of possible check