Lattice Boltzmann simulations of three-dimensional thermal convective flows at high Rayleigh number

We present numerical simulations of three-dimensional thermal convective flows in a cubic cell at high Rayleigh number using thermal lattice Boltzmann (LB) method. The thermal LB model is based on double distribution function approach, which consists of a D3Q19 model for the Navier-Stokes equations to simulate fluid flows and a D3Q7 model for the convection-diffusion equation to simulate heat transfer. Relaxation parameters are adjusted to achieve the isotropy of the fourth-order error term in the thermal LB model. Two types of thermal convective flows are considered: one is laminar thermal convection in side-heated convection cell, which is heated from one vertical side and cooled from the other vertical side; while the other is turbulent thermal convection in Rayleigh-B\'enard convection cell, which is heated from the bottom and cooled from the top. In side-heated convection cell, steady results of hydrodynamic quantities and Nusselt numbers are presented at Rayleigh numbers of $10^6$ and $10^7$, and Prandtl number of 0.71, where the mesh sizes are up to $257^3$; in Rayleigh-B\'enard convection cell, statistical averaged results of Reynolds and Nusselt numbers, as well as kinetic and thermal energy dissipation rates are presented at Rayleigh numbers of $10^6$, $3\times 10^6$, and $10^7$, and Prandtl numbers of 0.7 and 7, where the nodes within thermal boundary layer are around 8. Compared with existing benchmark data obtained by other methods, the present LB model can give consistent results.Comment: 33 pages, 8 figure

Turbulence of Dilute Polymer Solution

In fully developed three dimensional fluid turbulence the fluctuating energy is supplied at large scales, cascades through intermediate scales, and dissipates at small scales. It is the hallmark of turbulence that for intermediate scales, in the so called inertial range, the average energy flux is constant and independent of viscosity [1-3]. One very important question is how this range is altered, when an additional agent that can also transport energy is added to the fluid. Long-chain polymers dissolved at very small concentrations in the fluid are such an agent [4,5]. Based on prior work by de Gennes and Tabor [6,7] we introduce a theory that balances the energy flux through the turbulent cascade with that of the energy flux into the elastic degrees of freedom of the dilute long-chain polymer solution. We propose a refined elastic length scale, $r_\varepsilon$, which describes the effect of polymer elasticity on the turbulence energy cascade. Our experimental results agree excellently with this new energy flux balance theory.Comment: 15 pages, 5 figure

Role of weak measurements on states ordering and monogamy of quantum correlation

The information-theoretic definition of quantum correlation, e.g., quantum discord, is measurement dependent. By considering the more general quantum measurements, weak measurements, which include the projective measurement as a limiting case, we show that while weak measurements can enable one to capture more quantumness of correlation in a state, it can also induce other counterintuitive quantum effects. Specifically, we show that the general measurements with different strengths can impose different orderings for quantum correlations of some states. It can also modify the monogamous character for certain classes of states as well which may diminish the usefulness of quantum correlation as a resource in some protocols. In this sense, we say that the weak measurements play a dual role in defining quantum correlation.Comment: 6 pages, 5 figures, the final version as that published in Int. J. Theor. Phy

Suppression of long-wavelength CMB spectrum from the Hartle-Hawking wave function in Starobinsky-type inflation model

The lack of correlations on the large scale cosmic microwave background (CMB) anisotropy provides a potential window to probe beyond the standard inflationary scenario. In this paper, we investigate the primordial power spectrum based on the Hartle-Hawking (HH) no-boundary proposal for a homogeneous, isotropic, and spatially-closed universe that leads to a Starobinsky-type inflation after the classicalization. While we found that there is no suppression at large scales in the standard R + R^2 theory, we also found that it is possible to sufficiently suppress the large-scale power spectrum if a pre-inflation stage is introduced to the Starobinsky-type model. We calculate the C^TT_l correlation function and show that our proposal gives a better fit to the Planck CMB data. l This suggests that our universe might have begun with a compact HH state with a small positive curvature.Comment: 19 pages, 8 figure

Quantum Metrology via Repeated Quantum Nondemolition Measurements in "Photon Box"

In quantum metrology schemes, one generally needs to prepare $m$ copies of $N$ entangled particles, such as entangled photon states, and then they are detected in a destructive process to estimate an unknown parameter. Here, we present a novel experimental scheme for estimating this parameter by using repeated indirect quantum nondemolition measurements in the setup called "photon box". This interaction-based scheme is able to achieve the phase sensitivity scaling as $1/N$ with a Fock state of $N$ photons. Moreover, we only need to prepare one initial $N$-photon state and it can be used repetitively for $m$ trials of measurements. This new scheme is shown to sustain the quantum advantage for a much longer time than the damping time of Fock state and be more robust than the common strategy with exotic entangled states. To overcome the $2\pi/N$ periodic error in the estimation of the true parameter, we can employ a cascaded strategy by adding a real-time feedback interferometric layout.Comment: 5 pages, 3 figure

Tunable Band Topology Reflected by Fractional Quantum Hall States in Two-Dimensional Lattices

Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from the Hofstadter model and demonstrate that the band topology transitions can be realized by simply introducing tunable longer-range hopping. The rich phase diagram of band Chern numbers is obtained for the simple rational flux density and a classification of phases is presented. In the presence of interactions, the existence of fractional quantum Hall states in both |C|=1 and |C|>1 bands is confirmed, which can reflect the band topologies in different phases. In contrast, when our model reduces to a one-dimensional lattice, the ground states are crucially different from fractional quantum Hall states. Our results may provide insights into the study of new fractional quantum Hall states and experimental realizations of various topological phases in optical lattices.Comment: published version (6 pages, 6 figures, including a supplemental material

Quantum-enhanced metrology for multiple phase estimation with noise

We present a general framework to study the simultaneous estimation of multiple phases in the presence of noise as a discretized model for phase imaging. This approach can lead to nontrivial bounds of the precision for multiphase estimation. Our results show that simultaneous estimation (SE) of multiple phases is always better than individual estimation (IE) of each phase even in noisy environment. However with $d$ being the number of phases, the $O(d)$ advantage in the variance of the estimation, with which SE outperforms IE schemes for noiseless processes, may disappear asymptotically. When noise is low, those bounds recover the Heisenberg scale with the $O(d)$ advantage. The utility of the bound of multiple phase estimation for photon loss channels is exemplified.Comment: 9 pages, 2 figure

CP violation in B±→π±π+π−B^{\pm} \rightarrow \pi^{\pm}\pi^{+}\pi^{-} in the region with low invariant mass of one π+π−\pi^{+}\pi^{-} pair

Recently, the large CP asymmetries in $B^\pm\to\pi^\pm\pi^+\pi^-$ decays were found by the LHCb Collaboration to localize in the region $m_{\pi^+\pi^-}^2<0.4 \text{GeV}^2$. We find such large localized CP asymmetries may be due to the interference between a light scalar and $\rho^0(770)$ intermediate resonances. Consequently, we argue that the distribution of CP asymmetries in the Dalitz plots of three-body B decays could be very helpful for identifying the presence of the scalar resonance.Comment: 5 pages, 1 figure, 1 table, to be published on Physical Review

CP violation induced by the interference of scalar and vector resonances in three-body decays of bottom mesons

Large CP violation is an interesting phenomenon both theoretically and experimentally. Last year, LHCb Collaboration found in some three-body decays of bottom mesons that large CP violations appear in regions of the Dalitz plots that are not dominated by contributions from narrow resonances. In this paper, we present a mechanism which can induce such kind of large CP violations. In this mechanism, large localized CP asymmetries in phase space can be induced by the interference of two intermediate resonances with different spins. We also apply this mechanism to the decay channel $B^\pm\to K^\pm \pi^+\pi^-$.Comment: 11 pages, 1 figur

Formation of Transient Coronal Holes during Eruption of a Quiescent Filament and its Overlying Sigmoid

By using H$\alpha$, He I 10830, EUV and soft X-ray (SXR) data, we examined a filament eruption that occurred on a quiet-sun region near the center of the solar disk on 2006 January 12, which disturbed a sigmoid overlying the filament channel observed by the \emph{GOES-12} SXR Imager (SXI), and led to the eruption of the sigmoid. The event was associated with a partial halo coronal mass ejection (CME) observed by the Large Angle and Spectrometric Coronagraphs (LASCO) on board the Solar and Heliospheric Observatory (\emph{SOHO}), and resulted in the formation of two flare-like ribbons, post-eruption coronal loops, and two transient coronal holes (TCHs), but there were no significantly recorded \emph{GOES} or H$\alpha$ flares corresponding to the eruption. The two TCHs were dominated by opposite magnetic polarities and were located on the two ends of the eruptive sigmoid. They showed similar locations and shapes in He I 10830, EUV and SXR observations. During the early eruption phase, brightenings first appeared on the locations of the two subsequent TCHs, which could be clearly identified on He I 10830, EUV and SXR images. This eruption event could be explained by the magnetic flux rope model, and the two TCHs were likely to be the feet of the flux rope.Comment: 8 pages, 5 figures, accepted by Chja