Spontaneous symmetry breaking and quantum Hall valley ordering on the surface of topological hexaborides

A number of strongly correlated heavy fermion compounds, such as samarium (Sm), ytterbium (Yb), plutonium (Pu) hexaboride, are predicted to become topological insulators at low temperatures. These systems support massless Dirac fermions near certain (three) points of the surface Brillouin zone, hereafter referred to as the valleys. In strong perpendicular magnetic fields, the conical Dirac dispersions of these surface states quench onto three sets of Landau levels and we predict various possible hierarchies of incompressible quantum Hall states on the surface of hexaborides. In addition, we address the effects of strong electron-electron interaction within the surface zeroth Landau levels. Specifically, we show that depending on the relative strength of the long-range (Coulomb-type) and the finite-range (Hubbard-type) interactions the ground state can display either a valley-polarized or a valley-coherent distribution of electronic density. We also show that the transition between two valley-polarized states is always discontinuous, while that between a valley-polarized and a valley-coherent phase is continuous. The Zeeman splitting and/or an applied uniaxial strain on the surface can drive the system through various quantum phase transitions and place it in different broken-symmetry phases. Application of uniaxial strain is also shown to considerably modify the precise sequence of quantum Hall states. We also highlight the role of topology in determining the broken symmetry phases, disorder on the surface of topological hexaborides in strong magnetic fields.Comment: 14 pages, 7 figure

Fluctuations in mixtures of lamellar- and nonlamellar-forming lipids

We consider the role of nonlamellar-forming lipids in biological membranes by examining fluctuations, within the random phase approximation, of a model mixture of two lipids, one of which forms lamellar phases while the other forms inverted hexagonal phases. To determine the extent to which nonlamellar-forming lipids facilitiate the formation of nonlamellar structures in lipid mixtures, we examine the fluctuation modes and various correlation functions in the lamellar phase of the mixture. To highlight the role fluctuations can play, we focus on the lamellar phase near its limit of stability. Our results indicate that in the initial stages of the transition, undulations appear in the lamellae occupied by the tails, and that the nonlamellar-forming lipid dominates these undulations. The lamellae occupied by the head groups pinch off to make the tubes of the hexagonal phase. Examination of different correlations and susceptibilities makes quantitative the dominant role of the nonlamellar-forming lipids.Comment: 7 figures (better but larger in byte figures are available upon resuest), submitte

Revisit of cosmic age problem

We investigate the cosmic age problem associated with 9 extremely old globular clusters in M31 galaxy and 1 very old high-$z$ quasar APM 08279 + 5255 at $z=3.91$. These 9 globular clusters have not been used to study the cosmic age problem in the previous literature. By evaluating the age of the universe in the $\Lambda$CDM model with the observational constraints from the SNIa, the BAO, the CMB, and the independent $H_0$ measurements, we find that the existence of 5 globular clusters and 1 high-$z$ quasar are in tension (over 2$\sigma$ confidence level) with the current cosmological observations. So if the age estimates of these objects are correct, the cosmic age puzzle still remains in the standard cosmology. Moreover, we extend our investigations to the cases of the interacting dark energy models. It is found that although the introduction of the interaction between dark sectors can give a larger cosmic age, the interacting dark energy models still have difficulty to pass the cosmic age test.Comment: 11 pages, 5 figures, 1 table, accepted for publication in PR

Exploring the Latest Union2 SNIa Dataset by Using Model-Independent Parametrization Methods

We explore the cosmological consequences of the recently released Union2 sample of 557 Type Ia supernovae (SNIa). Combining this latest SNIa dataset with the Cosmic microwave background (CMB) anisotropy data from the Wilkinson Microwave Anisotropy Probe 7 year (WMAP7) observations and the baryon acoustic oscillation (BAO) results from the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7), we measure the dark energy density function $f(z)\equiv \rho_{de}(z)/\rho_{de}(0)$ as a free function of redshift. Two model-independent parametrization methods (the binned parametrization and the polynomial interpolation parametrization) are used in this paper. By using the $\chi^2$ statistic and the Bayesian information criterion, we find that the current observational data are still too limited to distinguish which parametrization method is better, and a simple model has advantage in fitting observational data than a complicated model. Moreover, it is found that all these parametrizations demonstrate that the Union2 dataset is still consistent with a cosmological constant at 1$\sigma$ confidence level. Therefore, the Union2 dataset is different from the Constitution SNIa dataset, which more favors a dynamical dark energy.Comment: 11 pages, 8 figures, 2 tables, accepted for publication in PR

How AD Can Help Solve Differential-Algebraic Equations

A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical solution. This is often done with the help of a computer algebra system. We show in two significant cases that it can be done efficiently by pure algorithmic differentiation. The first is the Dummy Derivatives method, here we give a mainly theoretical description, with tutorial examples. The second is the solution of a mechanical system directly from its Lagrangian formulation. Here we outline the theory and show several non-trivial examples of using the "Lagrangian facility" of the Nedialkov-Pryce initial-value solver DAETS, namely: a spring-mass-multipendulum system, a prescribed-trajectory control problem, and long-time integration of a model of the outer planets of the solar system, taken from the DETEST testing package for ODE solvers