Quantitative Description of V2O3V_2O_3 by the Hubbard Model in Infinite Dimensions

We show that the analytic single-particle density of states and the optical conductivity for the half-filled Hubbard model on the Bethe lattice in infinite dimensions describe quantitatively the behavior of the gap and the kinetic energy ratio of the correlated insulator $V_2O_3$. The form of the optical conductivity shows $\omega^{3/2}$ rising and is quite similar to the experimental data, and the density of states shows $\omega^{1/2}$ behavior near the band edges.Comment: 9 pages, revtex, 4 figures upon reques

Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian

Based on the technique of integration within an ordered product (IWOP) of operators we introduce the Fresnel operator for converting Caldirola-Kanai Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel operator with the parameters A,B,C,D corresponds to classical optical Fresnel transformation, these parameters are the solution to a set of partial differential equations set up in the above mentioned converting process. In this way the exact wavefunction solution of the Schr\"odinger equation governed by the Caldirola-Kanai Hamiltonian is obtained, which represents a squeezed number state. The corresponding Wigner function is derived by virtue of the Weyl ordered form of the Wigner operator and the order-invariance of Weyl ordered operators under similar transformations. The method used here can be suitable for solving Schr\"odinger equation of other time-dependent oscillators.Comment: 6 pages, 2 figure

Finite-size scaling of synchronized oscillation on complex networks

The onset of synchronization in a system of random frequency oscillators coupled through a random network is investigated. Using a mean-field approximation, we characterize sample-to-sample fluctuations for networks of finite size, and derive the corresponding scaling properties in the critical region. For scale-free networks with the degree distribution $P(k)\sim k^{-\gamma}$ at large $k$, we found that the finite size exponent $\bar{\nu}$ takes on the value 5/2 when $\gamma>5$, the same as in the globally coupled Kuramoto model. For highly heterogeneous networks ($3<\gamma <5$), $\bar{\nu}$ and the order parameter exponent $\beta$ depend on $\gamma$. The analytic expressions for these exponents obtained from the mean field theory are shown to be in excellent agreement with data from extensive numerical simulations.Comment: 7 page

Research for preparation of cation-conducting solids by high-pressure synthesis and other methods

It was shown that two body-centered-cubic skeleton structures, the Im3 KSbO3 phase and the defect-pyrochlore phase A(+)B2X6, do exhibit fast Na(+)-ion transport. The placement of anions at the tunnel intersection sites does not impede Na(+)-ion transport in (NaSb)3)(1/6 NaF), and may not in (Na(1+2x)Ta2 5F)(Ox). The activation energies are higher than those found in beta-alumina. There are two possible explanations for the higher activation energy: breathing of the bottleneck (site face or edge) through which the A(+) ions must pass on jumping from one site to another may be easier in a layer structure and/or A(+)-O bonding may be stronger in the cubic structures because the O(2-) ion bonds with two (instead of three) cations of the skeleton. If the former explanation is dominant, a lower activation energy may be achieved by optimizing the lattice parameter. If the latter is dominant, a new structural principle may have to be explored

Constraining the HI-Halo Mass Relation From Galaxy Clustering

We study the dependence of galaxy clustering on atomic gas mass using a sample of $\sim$16,000 galaxies with redshift in the range of $0.0025<z<0.05$ and HI mass of $M_{\rm HI}>10^8M_{\odot}$, drawn from the 70% complete sample of the Arecibo Legacy Fast ALFA survey. We construct subsamples of galaxies with $M_{\rm HI}$ above different thresholds, and make volume-limited clustering measurements in terms of three statistics: the projected two-point correlation function, the projected cross-correlation function with respect to a reference sample selected from the Sloan Digital Sky Survey, and the redshift-space monopole moment. In contrast to previous studies, which found no/weak HI-mass dependence, we find both the clustering amplitude on scales above a few Mpc and the bias factors to increase significantly with increasing HI mass for subsamples with HI mass thresholds above $10^9M_{\odot}$. For HI mass thresholds below $10^9M_{\odot}$, while the measurements have large uncertainties caused by the limited survey volume and sample size, the inferred galaxy bias factors are systematically lower than the minimum halo bias factor from mass-selected halo samples. The simple halo model, in which galaxy content is only determined by halo mass, has difficulties in interpreting the clustering measurements of the HI-selected samples. We extend the simple model by including the halo formation time as an additional parameter. A model that puts HI-rich galaxies into halos that formed late can reproduce the clustering measurements reasonably well. We present the implications of our best-fitting model on the correlation of HI mass with halo mass and formation time, as well as the halo occupation distributions and HI mass functions for central and satellite galaxies. These results are compared with the predictions from semi-analytic galaxy formation models and hydrodynamic galaxy formation simulations.Comment: Accepted for publication in ApJ. The 2PCF measurements are available at http://sdss4.shao.ac.cn/guoh

From the Complete Yang Model to Snyder's Model, de Sitter Special Relativity and Their Duality

By means of Dirac procedure, we re-examine Yang's quantized space-time model, its relation to Snyder's model, the de Sitter special relativity and their UV-IR duality. Starting from a dimensionless dS_5-space in a 5+1-d Mink-space a complete Yang model at both classical and quantum level can be presented and there really exist Snyder's model, the dS special relativity and the duality.Comment: 7 papge

Condensation of Hard Spheres Under Gravity: Exact Results in One Dimension

We present exact results for the density profile of the one dimensional array of N hard spheres of diameter D and mass m under gravity g. For a strictly one dimensional system, the liquid-solid transition occurs at zero temperature, because the close-pakced density, $\phi_c$, is one. However, if we relax this condition slightly such that $phi_c=1-\delta$, we find a series of critical temperatures T_c^i=mgD(N+1-i)/\mu_o with \mu_o=const, at which the i-th particle undergoes the liquid-solid transition. The functional form of the onset temperature, T_c^1=mgDN/\mu_o, is consistent with the previous result [Physica A 271, 192 (1999)] obtained by the Enskog equation. We also show that the increase in the center of mass is linear in T before the transition, but it becomes quadratic in T after the transition because of the formation of solid near the bottom

Neutrino masses, leptogenesis and dark matter in hybrid seesaw

We suggest a hybrid seesaw model where relatively ``light''right-handed neutrinos give no contribution to the neutrino mass matrix due to a special symmetry. This allows their Yukawa couplings to the standard model particles to be relatively strong, so that the standard model Higgs boson can decay dominantly to a left and a right-handed neutrino, leaving another stable right-handed neutrino as cold dark matter. In our model neutrino masses arise via the type-II seesaw mechanism, the Higgs triplet scalars being also responsible for the generation of the matter-antimatter asymmetry via the leptogenesis mechanism.Comment: 4 page

Reconsideration of Second Harmonic Generation from neat Air/Water Interface: Broken of Kleinman Symmetry from Dipolar Contribution

It has been generally accepted that there are significant quadrupolar and bulk contributions to the second harmonic generation (SHG) reflected from the neat air/water interface, as well as common liquid interfaces. Because there has been no general methodology to determine the quadrupolar and bulk contributions to the SHG signal from a liquid interface, this conclusion was reached based on the following two experimental phenomena. Namely, the broken of the macroscopic Kleinman symmetry, and the significant temperature dependence of the SHG signal from the neat air/water interface. However, because sum frequency generation vibrational spectroscopy (SFG-VS) measurement of the neat air/water interface observed no apparent temperature dependence, the temperature dependence in the SHG measurement has been reexamined and proven to be an experimental artifact. Here we present a complete microscopic analysis of the susceptibility tensors of the air/water interface, and show that dipolar contribution alone can be used to address the issue of broken of the macroscopic Kleinman symmetry at the neat air/water interface. Using this analysis, the orientation of the water molecules at the interface can be obtained, and it is consistent with the measurement from SFG-VS. Therefore, the key rationales to conclude significantly quadrupolar and bulk contributions to the SHG signal of the neat air/water interface can no longer be considered as valid as before. This new understanding of the air/water interface can shed light on our understanding of the nonlinear optical responses from other molecular interfaces as well