Lookahead Strategies for Sequential Monte Carlo

Based on the principles of importance sampling and resampling, sequential Monte Carlo (SMC) encompasses a large set of powerful techniques dealing with complex stochastic dynamic systems. Many of these systems possess strong memory, with which future information can help sharpen the inference about the current state. By providing theoretical justification of several existing algorithms and introducing several new ones, we study systematically how to construct efficient SMC algorithms to take advantage of the "future" information without creating a substantially high computational burden. The main idea is to allow for lookahead in the Monte Carlo process so that future information can be utilized in weighting and generating Monte Carlo samples, or resampling from samples of the current state.Comment: Published in at http://dx.doi.org/10.1214/12-STS401 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Transition density and pressure in hot neutron stars

Using the momentum-dependent MDI effective interaction for nucleons, we have studied the transition density and pressure at the boundary between the inner crust and liquid core of hot neutron stars. We find that their values are larger in neutrino-trapped neutron stars than in neutrino-free neutron stars. Furthermore, both are found to decrease with increasing temperature of a neutron star as well as increasing slope parameter of the nuclear symmetry energy, except that the transition pressure in neutrino-trapped neutron stars for the case of small symmetry energy slope parameter first increases and then decreases with increasing temperature. We have also studied the effect of the nuclear symmetry energy on the critical temperature above which the inner crust in a hot neutron star disappears and found that with increasing value of the symmetry energy slope parameter, the critical temperature decreases slightly in neutrino-trapped neutron stars but first decreases and then increases in neutrino-free neutron stars.Comment: 7 pages, 6 figures, version to appear in Phys. Rev.

Magic wavelengths for the 6s2 1S0−6s6p 3P1o6s^2\,^1S_0-6s6p\,^3P_1^o transition in ytterbium atom

The static and dynamic electric-dipole polarizabilities of the $6s^2\,^1S_0$ and $6s6p\,^3P_1^o$ states of Yb are calculated by using the relativistic ab initio method. Focusing on the red detuning region to the $6s^2\,^1S_0-6s6p\,^3P_1^o$ transition, we find two magic wavelengths at 1035.7(2) nm and 612.9(2) nm for the $6s^2\,^1S_0-6s6p\,^3P_1^o, M_J=0$ transition and three magic wavelengthes at 1517.68(6) nm, 1036.0(3) nm and 858(12) nm for the $6s^2\,^1S_0-6s6p\,^3P_1^o, M_J=\pm1$ transitions. Such magic wavelengths are of particular interest for attaining the state-insensitive cooling, trapping, and quantum manipulation of neutral Yb atom.Comment: 13 pages, 3 figure

Density slope of the nuclear symmetry energy from the neutron skin thickness of heavy nuclei

Expressing explicitly the parameters of the standard Skyrme interaction in terms of the macroscopic properties of asymmetric nuclear matter, we show in the Skyrme-Hartree-Fock approach that unambiguous correlations exist between observables of finite nuclei and nuclear matter properties. We find that existing data on neutron skin thickness $\Delta r_{np}$ of Sn isotopes give an important constraint on the symmetry energy $E_{sym}({\rho _{0}})$ and its density slope $L$ at saturation density ${\rho _{0}}$. Combining these constraints with those from recent analyses of isospin diffusion and double neutron/proton ratio in heavy-ion collisions at intermediate energies leads to a more stringent limit on $L$ approximately independent of $E_{sym}({\rho _{0}})$. The implication of these new constraints on the $\Delta r_{np}$ of $^{208}$Pb as well as the core-crust transition density and pressure in neutron stars is discussed.Comment: 18 pages, 9 figures, 1 table. Significantly expanded to include a number of details and discussions. Title shortened. Accepted version to appear in PR

Symmetry Reduction and Boundary Modes for Fe-Chains on an s-wave Superconductor

We investigate the superconducting phase diagram and boundary modes for a quasi-1D system formed by three Fe-Chains on an s-wave superconductor, motivated by the recent Princeton experiment. The $\vec l\cdot\vec s$ onsite spin-orbit term, inter-chain diagonal hopping couplings, and magnetic disorders in the Fe-chains are shown to be crucial for the superconducting phases, which can be topologically trivial or nontrivial in different parameter regimes. For the topological regime a single Majorana and multiple Andreew bound modes are obtained in the ends of the chain, while for the trivial phase only low-energy Andreev bound states survive. Nontrivial symmetry reduction mechanism induced by the $\vec l\cdot\vec s$ term, diagonal hopping couplings, and magnetic disorder is uncovered to interpret the present results. Our study also implies that the zero-bias peak observed in the recent experiment may or may not reflect the Majorana zero modes in the end of the Fe-chains.Comment: 5 pages, 4 figures; some minor errors are correcte