Loss of Exchange Symmetry in Multiqubit States under Ising Chain Evolution

Keeping in view of importance of exchange symmetry aspects in studies on spin squeezing of multiqubit states,we show that the one-dimensional Ising Hamiltonian with nearest neighbor interactions does not retain the exchange symmetry of initially symmetric multiqubit states.Specifically we show that among 4-qubit states obeying exchange symmetry,all states except W class(and their linear combination)lose their symmetry under time evolution with Ising Hamiltonian.Attributing the loss of symmetry of the initially symmetric states to rotational asymmetry of the one-dimensional Ising Hamiltonian with more than 3 qubits,we indicate that all N-qubit states(N>5)obeying permutation symmetry lose their symmetry after time evolution with Ising Hamiltonian.

Improved Retrieval of Sea Ice Thickness and Density from Laser Altimeter

The sensitivity of weather and climate system to sea ice thickness (SIT) in the Arctic is recognised from various studies. Decrease of SIT will affect atmospheric circulation, temperature, precipitation and wind speed in the Arctic and remotely. Ice thermodynamics and dynamic properties depend strongly on ice and snow thickness. The heat transfer through ice critically depends on ice thickness. Long term accurate SIT records with corresponding uncertainties are required for improved seasonal weather forecast and estimate of the sea ice mass balance. Satellite radar and Laser Altimeter (LA) provide long term records of sea ice freeboard. Assuming isostatic equilibrium, SIT is retrieved from the freeboard, extracted from radar altimeter (RA) or LA, where the snow depth, density, ice and water density are input variables in the equation for hydrostatic equilibrium to derive SIT from LA or RA. Different input variables (snow depth, density, ice and water density) with unknown accuracy have been applied from various authors to retrieve SIT and Sea Ice Draft (SID) from RA or LA, leading to not comparative results. Sea ice density dependence on ice type, thermodynamic properties and freeboard is confirmed with different studies. Sensitivity analyses confirm the great impact of sea ice density, snow depth and density on accuracy of the retrieved SIT and the importance of inserting variable ice density (VID) in the equation for hydrostatic equilibrium for more accurate SIT retrieval, weather and climate forecast. The impact of sea ice density and snow depth and density on retrieved SIT from the freeboard derived from LA and RA have been analyzed in this study using the equation for hydrostatic equilibrium, statistical and sensitivity analyses. An algorithm is developed to convert the freeboard, derived from LA in SIT, inserting VID in the equation for hydrostatic equilibrium. The algorithm is validated with field, laboratory studies and collocated SIT retrieved from RA on board Envisat. The accuracy of the developed algorithm is analyzed, using statistical and uncertainty analyses. It is found that the uncertainty of the retrieved SIT from LA is decreased 7.6 times (from rhi = 59 cm for fixed ice density) if variable ice density is inserted in the equation for hydrostatic equilibrium. The SIT, which has been retrieved from the freeboard derived from LA is validated with collocated SIT derived from RA2 on Envisat, using variable ice density. The bias of the mean SIT derived from LA and RA has been reduced from -1.1 m to about one millimeter when VID is applied to retrieve SIT from LA and RA. The results and algorithms, discussed in this paper are essential contribution to SIT and SID retrieval, satellite remote sensing, cryosphere, meteorology and improved weather and climate forecast.

Precision of future experiments measuring primordial tensor fluctuation

Recently the second phase of Background Imaging of Cosmic Extragalactic Polarization （BICEP2） claimed a detection of the tensor-to-scalar ratio （r） of primordial fluctuation at 50- confidence level. If it is true, this large and measurable amplitude （r - 0.2） of B-mode polarization indicates that it is possible to measure the shape of CMB B-mode polarization with future experiments. Given the current understanding of the experimental noise and foreground contamination, we forecast the precision of r and the tensor spectral index nt measurements from Planck, Spider and POLARBEAR with nt as a free parameter. We quantitatively determine the signal-to-noise of the measurement in r-nt parameter space for the three experiments. The forecasted signal-to-noise ratio of the B-mode polarization somewhat depends on r/t, but strongly depends on the true value of r.

Asymptotic solvers for ordinary differential equations with multiple frequencies

We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms,focusing on the case of multiple,non-commensurate frequencies.We derive an asymptotic expansion in inverse powers of the oscillatory parameter and use its truncation as an exceedingly effective means to discretize the differential equation in question.Numerical examples illustrate the effectiveness of the method.

QUADRATURE METHODS FOR HIGHLY OSCILLATORY SINGULAR INTEGRALS

We address the evaluation of highly oscillatory integrals,with power-law and logarithmic singularities.Such problems arise in numerical methods in engineering.Notably,the evaluation of oscillatory integrals dominates the run-time for wave-enriched boundary integral formulations for wave scattering,and many of these exhibit singularities.We show that the asymptotic behaviour of the integral depends on the integrand and its derivatives at the singular point of the integrand,the stationary points and the endpoints of the integral.A truncated asymptotic expansion achieves an error that decays faster for increasing frequency.Based on the asymptotic analysis,a Filon-type method is constructed to approximate the integral.Unlike an asymptotic expansion,the Filon method achieves high accuracy for both small and large frequency.Complex-valued quadrature involves interpolation at the zeros of polynomials orthogonal to a complex weight function.Numerical results indicate that the complex-valued Gaussian quadrature achieves the highest accuracy when the three methods are compared.However,while it achieves higher accuracy for the same number of function evaluations,it requires signi cant additional cost of computation of orthogonal polynomials and their zeros.

Observational constraints on running vacuum model

We investigate the power spectra of the CMB temperature and matter density in the running vacuum model(RVM) with the time-dependent cosmological constant of A=3 vH^2+ Λ_0, where H is the Hubble parameter. In this model, dark energy decreases in time and decays to both matter and radiation. By using the Markov chain Monte Carlo method, we constrain the model parameter v as well as the cosmological observables. Explicitly, we obtain v ≤1.54× 10^(-4)(68% confidence level) in the RVM with the best-fit χ_(RVM)~2 =13968.8, which is slightly smaller thanχ_(ΛCDM)~2= 13969.8 in the ΛCDM model of v = 0.

Inflation, Cosmic Perturbations and Non-Gaussianities

We review the theory of inflationary perturbations. Perturbations at both linear and nonlinear orders are reviewed. We also review a variety of inflation models, emphasizing their signatures on cosmic perturbations.