Figure of Merit for Dark Energy Constraints from Current Observational Data

Choosing the appropriate figure of merit (FoM) for dark energy (DE) constraints is key in comparing different DE experiments. Here we show that for a set of DE parameters {f_i}, it is most intuitive to define FoM = 1/\sqrt{Cov(f1,f2,f3,...)}, where Cov(f1,f2,f3,...) is the covariance matrix of {f_i}. The {f_i} should be minimally correlated. We demonstrate two useful choices of {f_i} using 182 SNe Ia (compiled by Riess et al. 2007), [R(z_*), l_a(z_*), \Omega_b h^2] from the five year Wilkinson Microwave Anisotropy Probe (WMAP) observations, and SDSS measurement of the baryon acoustic oscillation (BAO) scale, assuming the HST prior of H_0=72+/-8 km/s Mpc^{-1} and without assuming spatial flatness. We find that the correlation of (w_0,w_{0.5}) [w_0=w_X(z=0), w_{0.5}=w_X(z=0.5), w_X(a) = 3w_{0.5}-2w_0+3(w_0-w_{0.5})a] is significantly smaller than that of (w_0,w_a) [w_X(a)=w_0+(1-a)w_a]. In order to obtain model-independent constraints on DE, we parametrize the DE density function X(z)=\rho_X(z)/\rho_X(0) as a free function with X_{0.5}, X_{1.0}, and X_{1.5} [values of X(z) at z=0.5, 1.0, and 1.5] as free parameters estimated from data. If one assumes a linear DE equation of state, current data are consistent with a cosmological constant at 68% C.L. If one assumes X(z) to be a free function parametrized by (X_{0.5}, X_{1.0}, X_{1.5}), current data deviate from a cosmological constant at z=1 at 68% C.L., but are consistent with a cosmological constant at 95% C.L.. Future DE experiments will allow us to dramatically increase the FoM of constraints on (w_0,w_{0.5}) and of (X_{0.5}, X_{1.0}, X_{1.5}). This will significantly shrink the DE parameter space to enable the discovery of DE evolution, or the conclusive evidence for a cosmological constant.Comment: 7 pages, 3 color figures. Submitte

Spin and Orbital Splitting in Ferromagnetic Contacted Single Wall Carbon Nanotube Devices

We observed the coulomb blockade phenomena in ferromagnetic contacting single wall semiconducting carbon nanotube devices. No obvious Coulomb peaks shift was observed with existing only the Zeeman splitting at 4K. Combining with other effects, the ferromagnetic leads prevent the orbital spin states splitting with magnetic field up to 2 Tesla at 4K. With increasing magnetic field further, both positive or negative coulomb peaks shift slopes are observed associating with clockwise and anticlockwise orbital state splitting. The strongly suppressed/enhanced of the conductance has been observed associating with the magnetic field induced orbital states splitting/converging

Beating the PNS attack in practical quantum cryptography

In practical quantum key distribution, weak coherent state is often used and the channel transmittance can be very small therefore the protocol could be totally insecure under the photon-number-splitting attack. We propose an efficient method to verify the upper bound of the fraction of counts caused by multi-photon pluses transmitted from Alice to Bob, given whatever type of Eve's action. The protocol simply uses two coherent states for the signal pulses and vacuum for decoy pulse. Our verified upper bound is sufficiently tight for QKD with very lossy channel, in both asymptotic case and non-asymptotic case. The coherent states with mean photon number from 0.2 to 0.5 can be used in practical quantum cryptography. We show that so far our protocol is the $only$ decoy-state protocol that really works for currently existing set-ups.Comment: So far this is the unique decoy-state protocol which really works efficiently in practice. Prior art results are commented in both main context and the Appendi

Analytical Results For The Steady State Of Traffic Flow Models With Stochastic Delay

Exact mean field equations are derived analytically to give the fundamental diagrams, i.e., the average speed - car density relations, for the Fukui-Ishibashi one-dimensional traffic flow cellular automaton model of high speed vehicles $(v_{max}=M>1)$ with stochastic delay. Starting with the basic equation describing the time evolution of the number of empty sites in front of each car, the concepts of inter-car spacings longer and shorter than $M$ are introduced. The probabilities of having long and short spacings on the road are calculated. For high car densities $(\rho \geq 1/M)$, it is shown that inter-car spacings longer than $M$ will be shortened as the traffic flow evolves in time, and any initial configurations approach a steady state in which all the inter-car spacings are of the short type. Similarly for low car densities $(\rho \leq 1/M)$, it can be shown that traffic flow approaches an asymptotic steady state in which all the inter-car spacings are longer than $M-2$. The average traffic speed is then obtained analytically as a function of car density in the asymptotic steady state. The fundamental diagram so obtained is in excellent agreement with simulation data.Comment: 12 pages, latex, 2 figure

Integro-differential diffusion equation for continuous time random walk

In this paper we present an integro-differential diffusion equation for continuous time random walk that is valid for a generic waiting time probability density function. Using this equation we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential, and a combination of power law and generalized Mittag-Leffler function. We show that for the case of the exponential waiting time probability density function a normal diffusion is generated and the probability density function is Gaussian distribution. In the case of the combination of a power-law and generalized Mittag-Leffler waiting probability density function we obtain the subdiffusive behavior for all the time regions from small to large times, and probability density function is non-Gaussian distribution.Comment: 12 page

A decoy-state protocol for quantum cryptography with 4 intensities of coherent states

In order to beat any type of photon-number-splitting attack, we propose a protocol for quantum key distributoin (QKD) using 4 different intensities of pulses. They are vacuum and coherent states with mean photon number $\mu,\mu'$ and $\mu_s$. $\mu_s$ is around 0.55 and this class of pulses are used as the main signal states. The other two classes of coherent states ($\mu,\mu'$) are also used signal states but their counting rates should be studied jointly with the vacuum. We have shown that, given the typical set-up in practice, the key rate from the main signal pulses is quite close to the theoretically allowed maximal rate in the case given the small overall transmittance of $10^{-4}$

Singlet-Triplet Physics and Shell Filling in Carbon Nanotube Double Quantum Dots

An artifcial two-atomic molecule, also called a double quantum dot (DQD), is an ideal system for exploring few electron physics. Spin-entanglement between just two electrons can be explored in such systems where singlet and triplet states are accessible. These two spin-states can be regarded as the two states in a quantum two-state system, a so-called singlet-triplet qubit. A very attractive material for realizing spin based qubits is the carbon nanotube (CNT), because it is expected to have a very long spin coherence time. Here we show the existence of a gate-tunable singlet-triplet qubit in a CNT DQD. We show that the CNT DQD has clear shell structures of both four and eight electrons, with the singlet-triplet qubit present in the four-electron shells. We furthermore observe inelastic cotunneling via the singlet and triplet states, which we use to probe the splitting between singlet and triplet, in good agreement with theory.Comment: Supplement available at: http://www.fys.ku.dk/~hij/public/singlet-triple_supp.pd

The Fundamental Plane of Gamma-ray Globular Clusters

We have investigated the properties of a group of $\gamma$-ray emitting globular clusters (GCs) which have recently been uncovered in our Galaxy. By correlating the observed $\gamma$-ray luminosities $L_{\gamma}$ with various cluster properties, we probe the origin of the high energy photons from these GCs. We report $L_{\gamma}$ is positively correlated with the encounter rate $\Gamma_{c}$ and the metalicity $\left[{\rm Fe/H}\right]$ which place an intimate link between the gamma-ray emission and the millisecond pulsar population. We also find a tendency that $L_{\gamma}$ increase with the energy densities of the soft photon at the cluster location. Furthermore, the two-dimensional regression analysis suggests that $L_{\gamma}$, soft photon densities, and $\Gamma_{c}$/$\left[{\rm Fe/H}\right]$ possibly span fundamental planes which potentially provide better predictions for the $\gamma$-ray properties of GCs.Comment: 17 pages, 4 figures, 3 tables, published in Ap