Many cosmological measurements today suggest that the Universe is expanding at a constant rate. This is inferred from the observed age versus redshift relationship and various distance indicators, all of which point to a cosmic equation of state (EoS) p = −ρ/3, where ρ and p are, respectively, the total energy density and pressure of the cosmic fluid. It has recently been shown that this result is not a coincidence and simply confirms the fact that the symmetries in the Friedmann–Robertson–Walker (FRW) metric appear to be viable only for a medium with zero active mass, i.e., ρ+ 3p = 0. In their latest paper, however, Kim, Lasenby and Hobson (2016) have provided what they believe to be a counter argument to this conclusion. Here, we show that these authors are merely repeating the conventional mistake of incorrectly placing the observer simultaneously in a comoving frame, where the lapse function gtt is coordinate dependent when ρ+ 3p≠0, and a supposedly different, freefalling frame, in which gtt = 1, implying no time dilation. We demonstrate that the Hubble flow is not inertial when ρ+ 3p≠0, so the comoving frame is generally not in free fall, even though in FRW, the comoving and free-falling frames are supposed to be identical at every spacetime point. So this confusion of frames not only constitutes an inconsistency with the fundamental tenets of general relativity but, additionally, there is no possibility of using a gauge transformation to select a set of coordinates for which gtt = 1 when ρ+ 3p≠0.
By using type Ia supernovae (SNIa) to provide the luminosity distance (LD) directly, which depends on the value of the Hubble constant H0 = 100h km·s−1·Mpc−1, and the angular diameter distance from galaxy clusters or baryon acoustic oscillations (BAOs) to give the derived LD according to the distance duality relation, we propose a model-independent method to determine h from the fact that different observations should give the same LD at a given redshift. Combining the Sloan Digital Sky Survey II (SDSS-II) SNIa from the MLCS2k2 light curve fit and galaxy cluster data, we find that at the 1σ confidence level (CL), h=0.5867±0.0303 for the sample of the elliptical β model for galaxy clusters, and h=0.6199±0.0293 for that of the sphericall β model. The former is smaller than the values from other observations, whereas the latter is consistent with the Planck result at the 2σ CL and agrees very well with the value reconstructed directly from the H(z) data. With the SDSS-II SNIa and BAO measurements, a tighter constraint, h = 0.6683±0.0221, is obtained. For comparison, we also consider the Union 2.1 SNIa from the SALT2 light curve fitting. The results from the Union 2.1 SNIa are slightly larger than those from the SDSS-II SNIa, and the Union 2.1 SNIa+ BAOs give the tightest value. We find that the values from SNIa+ BAOs are quite consistent with those from the Planck and the BAOs, as well as the local measurement from Cepheids and very-low-redshift SNIa.
Single-crystal erbium silicate nanowires have attracted considerable attention because of their high optical gain. In this work, we report the controlled synthesis of silicon-erbium ytterbium silicate coreshell nanowires and fine-tuning the erbium mole fraction in the shell from x=0.3 to x=1.0, which corresponds to changing the erbium concentration from 4.8×1021 to 1.6×1022 cm−3. By controlling and properly optimizing the composition of erbium and ytterbium in the nanowires, we can effectively suppress upconversion photoluminescence while simultaneously enhancing near-infrared emission. The composition-optimized nanowires have very long photoluminescence lifetimes and large emission crosssections, which contribute to the high optical gain that we observed. We suspended these concentrationoptimized nanowires in the air to measure and analyze their propagation loss and optical gain in the near-infrared communication band. Through systematic measurements using wires with different core sizes, we obtained a maximum net gain of 20±8 dB·mm−1, which occurs at a wavelength of 1534 nm, for a nanowire with a diameter of 600 nm and a silicon core diameter of 300 nm.
Nanoscale plasmonic systems combine the advantages of optical frequencies with those of small spatial scales, circumventing the limitations of conventional photonic systems by exploiting the strong field confinement of surface plasmons. As a result of this miniaturization to the nanoscale, electron microscopy techniques are the natural investigative methods of choice. Recent years have seen the development of a number of electron microscopy techniques that combine the use of electrons and photons to enable unprecedented views of surface plasmons in terms of combined spatial, energy, and time resolution. This review aims to provide a comparative survey of these different approaches from an experimental viewpoint by outlining their respective experimental domains of suitability and highlighting their complementary strengths and limitations as applied to plasmonics in particular.
Graphene has attracted extensive research interest in recent years because of its fascinating physical properties and its potential for various applications. The band structure or electronic properties of graphene are very sensitive to its geometry, size, and edge structures, especially when the size of graphene is below the quantum confinement limit. Graphene nanoribbons (GNRs) can be used as a model system to investigate such structure-sensitive parameters. In this review, we examine the fabrication of GNRs via both top-down and bottom-up approaches. The edge-related electronic and transport properties of GNRs are also discussed.
The band structure and effective mass of disordered chalcopyrite photovoltaic materials Cu1−xAgxGaX2 (X = S, Se) are investigated by density functional theory. Special quasirandom structures are used to mimic local atomic disorders at Cu/Ag sites. A local density plus correction method is adopted to obtain correct semiconductor band gaps for all compounds. The bandgap anomaly can be seen for both sulfides and selenides, where the gap values of Ag compounds are larger than those of Cu compounds. Band gaps can be modulated from 1.63 to 1.78 eV for Cu1−xAgxGaSe2, and from 2.33 to 2.64 eV for Cu1−xAgxGaS2. The band gap minima and maxima occur at around x= 0.5 and x= 1, respectively, for both sulfides and selenides. In order to show the transport properties of Cu1−xAgxGaX2, the effective mass is shown as a function of disordered Ag concentration. Finally, detailed band structures are shown to clarify the phonon momentum needed by the fundamental indirect-gap transitions. These results should be helpful in designing high-efficiency photovoltaic devices, with both better absorption and high mobility, by Ag-doping in CuGaX2.
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture), that can be put into correspondence with the usual Hamilton–Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamiltonian–Lagrange picture, defined on the Hamilton–Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton–Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton–Lagrange picture can be generated by variations along geodesics in the geometrical picture and establish a correspondence which provides a basis for understanding how the instability in the geometrical picture is manifested in the instability of the the original Hamiltonian motion.
Ultraslow-light effects in two-dimensional hexagonal-lattice coupled waveguide with moon-like scatterers were theoretically studied using the plane-wave expansion method. For symmetric structures, simulations showed that slow light with high group index can be achieved by shifting the scatterers and adjusting the radius of moon-like scatterers. The maximum group index was over 8.0×104. For asymmetric structures, simulations showed that slow light with flat band and high group index can be obtained by shifting the scatterers, adjusting the radius of moon-like scatterers, and rotating the scatterers. The maximum group index was over 5.7×105 with a “saddle-like” relationship between the frequency and group index.
We study fundamental modes trapped in a rotating ring with a saturated nonlinear double-well potential. This model, which is based on the nonlinear Schrödinger equation, can be constructed in a twisted waveguide pipe in terms of light propagation, or in a Bose–Einstein condensate (BEC) loaded into a toroidal trap under a combination of a rotating-out-of-phase linear potential and nonlinear pseudopotential induced by means of a rotating optical field and the Feshbach resonance. Three types of fundamental modes are identified in this model, one symmetric and the other two asymmetric. The shape and stability of the modes and the transitions between different modes are investigated in the first rotational Brillouin zone. A similar model used a Kerr medium to build its nonlinear potential, but we replace it with a saturated nonlinear medium. The model exhibits not only symmetry breaking, but also symmetry recovery. A specific type of unstable asymmetric mode is also found, and the evolution of the unstable asymmetric mode features Josephson oscillation between two linear wells. By considering the model as a configuration of a BEC system, the ground state mode is identified among these three types, which characterize a specific distribution of the BEC atoms around the trap.
Controlling the balanced gain and loss in a
We formulate an irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk (SAW), which violates the detailed balance condition and satisfies the balance condition. Its performance improves significantly compared to that of the Berretti–Sokal algorithm, which is a variant of the Metropolis–Hastings method. The gained efficiency increases with spatial dimension (D), from approximately 10 times in 2D to approximately 40 times in 5D. We simulate the SAW on a 5D hypercubic lattice with periodic boundary conditions, for a linear system with a size up to L= 128, and confirm that as for the 5D Ising model, the finite-size scaling of the SAW is governed by renormalized exponents, υ*= 2/d and γ/υ*= d/2. The critical point is determined, which is approximately 8 times more precise than the best available estimate.
Quantum computing has undergone rapid development in recent years. Owing to limitations on scalability, personal quantum computers still seem slightly unrealistic in the near future. The first practical quantum computer for ordinary users is likely to be on the cloud. However, the adoption of cloud computing is possible only if security is ensured. Homomorphic encryption is a cryptographic protocol that allows computation to be performed on encrypted data without decrypting them, so it is well suited to cloud computing. Here, we first applied homomorphic encryption on IBM’s cloud quantum computer platform. In our experiments, we successfully implemented a quantum algorithm for linear equations while protecting our privacy. This demonstration opens a feasible path to the next stage of development of cloud quantum information technology.
By coupling with a qubit, we demonstrate that qubit decoherence can unambiguously detect the occurrence of ground-state degeneracy in many-body systems. We first demonstrate universality using the two-band model. Consequently, several exemplifications, focused on topological condensed matter systems in one, two, and three dimensions, are presented to validate our proposal. The key point is that qubit decoherence varies significantly when energy bands touch each other at the Fermi surface. In addition, it can partially reflect the degeneracy inside the band. This feature implies that qubit decoherence can be used for reliable diagnosis of ground-state degeneracy.
In a series of recent papers [
In this paper we provide a thorough derivation from principles that in the most general case the graph of the quantum cellular automaton is the Cayley graph of a finitely presented group, and showing how for the case corresponding to Euclidean emergent space (where the group resorts to an Abelian one) the automata leads to Weyl, Dirac and Maxwell field dynamics in the relativistic limit. We conclude with some perspectives towards the more general scenario of non-linear automata for interacting quantum field theory.