Holographic Dark Energy Characterized by the Total Comoving Horizon and Insights to Cosmological Constant and Coincidence Problem

The observed acceleration of the present universe is shown to be well explained by the holographic dark energy characterized by the total comoving horizon of the universe ($\eta$HDE). It is of interest to notice that the very large primordial part of the comoving horizon generated by the inflation of early universe makes the $\eta$HDE behave like a cosmological constant. As a consequence, both the fine-tuning problem and the coincidence problem can reasonably be understood with the inflationary universe and holographical principle. We present a systematic analysis and obtain a consistent cosmological constraint on the $\eta$HDE model based on the recent cosmological observations. It is found that the $\eta$HDE model gives the best-fit result $\Omega_{m0}=0.270$ ($\Omega_{de0}=0.730$) and the minimal $\chi^2_{min}=542.915$ which is compatible with $\chi^2_{\Lambda {\rm CDM}}=542.919$ for the $\Lambda$CDM model.Comment: 17 pages, 4 figures, two eqs. (26)(27) added for the consistent approximate solution of dark energy in early universe, references added, published version in PR

Generation of 3-Dimensional graph state with Josephson charge qubits

On the basis of generations of 1-dimensional and 2-dimensional graph states, we generate a 3-dimensional N3-qubit graph state based on the Josephson charge qubits. Since any two charge qubits can be selectively and effectively coupled by a common inductance, the controlled phase transform between any two-qubit can be performed. Accordingly, we can generate arbitrary multi-qubit graph states corresponding to arbitrary shape graph, which meet the expectations of various quantum information processing schemes. All the devices in the scheme are well within the current technology. It is a simple, scalable and feasible scheme for the generation of various graph states based on the Josephson charge qubits.Comment: 4 pages, 4 figure

Kinetics of catalysis with surface disorder

We study the effects of generalised surface disorder on the monomer-monomer model of heterogeneous catalysis, where disorder is implemented by allowing different adsorption rates for each lattice site. By mapping the system in the reaction-controlled limit onto a kinetic Ising model, we derive the rate equations for the one and two-spin correlation functions. There is good agreement between these equations and numerical simulations. We then study the inclusion of desorption of monomers from the substrate, first by both species and then by just one, and find exact time-dependent solutions for the one-spin correlation functions.Comment: LaTex, 19 pages, 1 figure included, requires epsf.st

Cosmological Constraint and Analysis on Holographic Dark Energy Model Characterized by the Conformal-age-like Length

We present a best-fit analysis on the single-parameter holographic dark energy model characterized by the conformal-age-like length, $L=\frac{1}{a^4(t)}\int_0^tdt' a^3(t')$. Based on the Union2 compilation of 557 supernova Ia data, the baryon acoustic oscillation results from the SDSS DR7 and the cosmic microwave background radiation data from the WMAP7, we show that the model gives the minimal $\chi^2_{min}=546.273$, which is comparable to $\chi^2_{\Lambda{\rm CDM}}=544.616$ for the $\Lambda$CDM model. The single parameter $d$ concerned in the model is found to be $d=0.232\pm 0.006\pm 0.009$. Since the fractional density of dark energy $\Omega_{de}\sim d^2a^2$ at $a \ll 1$, the fraction of dark energy is naturally negligible in the early universe, $\Omega_{de} \ll 1$ at $a \ll 1$. The resulting constraints on the present fractional energy density of matter and the equation of state are \Omega_{m0}=0.286^{+0.019}_{-0.018}^{+0.032}_{-0.028} and w_{de0}=-1.240^{+0.027}_{-0.027}^{+0.045}_{-0.044} respectively. The model leads to a slightly larger fraction of matter comparing to the $\Lambda$CDM model. We also provide a systematic analysis on the cosmic evolutions of the fractional energy density of dark energy, the equation of state of dark energy, the deceleration parameter and the statefinder. It is noticed that the equation of state crosses from $w_{de}>-1$ to $w_{de}<-1$, the universe transits from decelerated expansion ($q>0$) to accelerated expansion ($q<0$) recently, and the statefinder may serve as a sensitive diagnostic to distinguish the CHDE model with the $\Lambda$CDM model.Comment: 17 pages, 5 figures, minor changes for the fitting data, references adde

Series expansions of the percolation probability for directed square and honeycomb lattices

We have derived long series expansions of the percolation probability for site and bond percolation on directed square and honeycomb lattices. For the square bond problem we have extended the series from 41 terms to 54, for the square site problem from 16 terms to 37, and for the honeycomb bond problem from 13 terms to 36. Analysis of the series clearly shows that the critical exponent $\beta$ is the same for all the problems confirming expectations of universality. For the critical probability and exponent we find in the square bond case, $q_c = 0.3552994\pm 0.0000010$, $\beta = 0.27643\pm 0.00010$, in the square site case $q_c = 0.294515 \pm 0.000005$, $\beta = 0.2763 \pm 0.0003$, and in the honeycomb bond case $q_c = 0.177143 \pm 0.000002$, $\beta = 0.2763 \pm 0.0002$. In addition we have obtained accurate estimates for the critical amplitudes. In all cases we find that the leading correction to scaling term is analytic, i.e., the confluent exponent $\Delta = 1$.Comment: LaTex with epsf, 26 pages, 2 figures and 2 tables in Postscript format included (uufiled). LaTeX version of tables also included for the benefit of those without access to PS printers (note that the tables should be printed in landscape mode). Accepted by J. Phys.

Scaling of the Equilibrium Magnetization in the Mixed State of Type-II Superconductors

We discuss the analysis of mixed-state magnetization data of type-II superconductors using a recently developed scaling procedure. It is based on the fact that, if the Ginzburg-Landau parameter kappa does not depend on temperature, the magnetic susceptibility is a universal function of H/H_c2(T), leading to a simple relation between magnetizations at different temperatures. Although this scaling procedure does not provide absolute values of the upper critical fieldH_c2(T), its temperature variation can be established rather accurately. This provides an opportunity to validate theoretical models that are usually employed for the evaluation of H_c2(T) from equilibrium magnetization data. In the second part of the paper we apply this scaling procedure for a discussion of the notorious first order phase transition in the mixed state of high temperature superconductors. Our analysis, based on experimental magnetization data available in the literature, shows that the shift of the magnetization accross the transition may adopt either sign, depending on the particular chosen sample. We argue that this observation is inconsistent with the interpretation that this transition always represents the melting transition of the vortex lattice.Comment: 18 pages, 12 figure

Path-integral representation for a stochastic sandpile

We introduce an operator description for a stochastic sandpile model with a conserved particle density, and develop a path-integral representation for its evolution. The resulting (exact) expression for the effective action highlights certain interesting features of the model, for example, that it is nominally massless, and that the dynamics is via cooperative diffusion. Using the path-integral formalism, we construct a diagrammatic perturbation theory, yielding a series expansion for the activity density in powers of the time.Comment: 22 pages, 6 figure

Self-Consistent Relativistic Calculation of Nucleon Mean Free Path

We present a fully self-consistent and relativistic calculation of the nucleon mean free path in nuclear matter and finite nuclei. Starting from the Bonn potential, the Dirac-Brueckner-Hartree-Fock results for nuclear matter are parametrized in terms of an effective $\sigma$-$\omega$ Lagrangian suitable for the relativistic density-dependent Hartree-Fock (RDHF) approximation. The nucleon mean free path in nuclear matter is derived from this effective Lagrangian taking diagrams up to fourth-order into account. For the nucleon mean free path in finite nuclei, we make use of the density determined by the RDHF calculation in the local density approximation. Our microscopic results are in good agreement with the empirical data and predictions by Dirac phenomenology.Comment: 16 pages RevTex and 6 figures (paper, available upon request from [email protected]) UI-NTH-931