The Tilt of Primordial Gravitational Waves Spectra from BICEP2

In this paper we constrain the tilt of the spectra of primordial gravitational waves from Background Imaging of Cosmic Extragalactic Polarization (BICEP2) data only. We find $r=0.21_{-0.10}^{+0.04}$ and $n_t=-0.06_{-0.23}^{+0.25}$ (at $68\%$ C.L.) which implies that a scale-invariant primordial gravitational waves spectra is consistent with BICEP2 nicely. Our results provide strong evidence for supporting inflation model, and the alternative models, for example the ekpyrotic model which predicts $n_t=2$, are ruled out at more than $5\sigma$ significance.Comment: 3 pages, 1 figur

An accurate determination of the Hubble constant from Baryon Acoustic Oscillation datasets

Even though the Hubble constant cannot be significantly determined by the low-redshift Baryon Acoustic Oscillation (BAO) data alone, it can be tightly constrained once the high-redshift BAO data are combined. Combining BAO data from 6dFGS, BOSS DR11 clustering of galaxies, WiggleZ and $z=2.34$ from BOSS DR11 quasar Lyman-$\alpha$ forest lines, we get $H_0=68.17^{+1.55}_{-1.56}$ km s$^{-1}$ Mpc$^{-1}$. In addition, adopting the the simultaneous measurements of $H(z)$ and $D_A(z)$ from the two-dimensional two-point correlation function from BOSS DR9 CMASS sample and two-dimensional matter power spectrum from SDSS DR7 sample, we obtain $H_0=68.11\pm1.69$ km s$^{-1}$ Mpc$^{-1}$. Finally, combining all of the BAO datasets, we conclude $H_0=68.11\pm 0.86$ km s$^{-1}$ Mpc$^{-1}$, a 1.3% determination.Comment: 13 pages, 5 figures, 2 table

Constraint on inflation model from BICEP2 and WMAP 9-year data

Even though Planck data released in 2013 (P13) is not compatible with Background Imaging of Cosmic Extragalactic Polarization (B2) and some local cosmological observations, including Supernova Legacy Survey (SNLS) samples and $H_0$ prior from Hubble Space Telescope (HST) etc, Wilkinson Microwaves Anisotropy Probe 9-year data (W9) is consistent with all of them in the base six-parameter $\Lambda$CDM+tensor cosmology quite well. In this letter, we adopt the combinations of B2+W9 and B2+W9+SNLS+BAO+HST to constrain the cosmological parameters in the base six-parameter $\Lambda$CDM+tensor model with $n_t=-r/8$, where r and $n_t$ are the tensor-to-scalar ratio and the tilt of relic gravitational wave spectrum, and BAO denotes Baryon Acoustic Oscillation. We find that the Harrison-Zel'dovich (HZ) scale invariant scalar power spectrum is consistent with both data combinations, chaotic inflation is marginally disfavored by the data at around $2\sigma$ level, but the power-law inflation model and the inflation model with inverse power-law potential can fit the data nicely.Comment: 4 pages, 1 figure; inflation model with power-law potential added and refs adde

The Dark Side of the Universe after Planck

Recently released Planck data implies a smaller Hubble constant $H_0$ than that from Hubble Space Telescope project (HST) and a larger percentage of the matter components $\Omega_m$ compared to Supernova Legacy Survey (SNLS) in $\Lambda$CDM model. In this paper we found that even though the tension on $H_0$ between Planck and HST can be relaxed if the dark radiation is introduced ($\Delta N_{\rm eff}=0.536_{-0.224}^{+0.229}$ at $68\%$ CL from the datasets of Planck+WMAP Polarization (WP)+baryon acoustic oscillation (BAO)+the combination of supernova Union2.1 compilation of 580 SNe (Union2.1)+HST), $\Omega_m$ from Planck is still not nicely compatible with that from SNLS. The tensions between Planck and other astrophysical datasets can be significantly relaxed in $w$CDM model, and the combination of these datasets prefers a phantom-like dark energy at more than $95\%$ CL: $w=-1.15\pm 0.07$ and $w=-1.16\pm 0.06$ at $68\%$ CL from Planck+WP+BAO+Union2.1+HST and Planck+WP+BAO+SNLS+HST respectively. From the statistical point of view, there is no evidence for a time-evolving equation of state ($\Delta \chi^2=-0.3$ compared to a constant equation of state for the combination of Planck+WP+BAO+SNLS+HST).Comment: 7 pages, 11 figures; refs added; version accepted for publication in Phys.Rev.

Destruction of Lagrangian torus for positive definite Hamiltonian systems

For an integrable Hamiltonian $H_0=1/2\sum_{i=1}^dy_i^2$ $(d\geq 2)$, we show that any Lagrangian torus with a given unique rotation vector can be destructed by arbitrarily $C^{2d-\delta}$-small perturbations. In contrast with it, it has been shown that KAM torus with constant type frequency persists under $C^{2d+\delta}$-small perturbations.Comment: accepted by Geometric and Functional Analysis (GAFA). arXiv admin note: substantial text overlap with arXiv:1208.284

Coherent dynamics of a qubit-oscillator system in a noisy environment

We investigate the non-Markovian dynamics of a qubit-oscillator system embedded in a noisy environment by employing the hierarchical equations of motion approach. It is found that the decoherence rate of the whole qubit-oscillator-bath system can be significantly suppressed by enhancing the coupling strength between the qubit and the harmonic oscillator. Moreover, we find that the non-Markovian memory character of the bath is able to facilitate a robust quantum coherent dynamics in this qubit-oscillator-bath system. Our findings may be used to engineer some tunable coherent manipulations in mesoscopic quantum circuits

Arnold diffusion in nearly integrable Hamiltonian systems of arbitrary degrees of freedom

In this paper Arnold diffusion is proved to be a generic phenomenon in nearly integrable convex Hamiltonian systems with arbitrarily many degrees of freedom: H(x,y)=h(y)+\eps P(x,y), \qquad x\in\mathbb{T}^n,\ y\in\mathbb{R}^n,\quad n\geq 3. Under typical perturbation \eps P, the system admits "connecting" orbit that passes through any finitely many prescribed small balls in the same energy level $H^{-1}(E)$ provided $E>\min h$.Comment: 87 pages, 11 figures. Comments welcome! This is the solution of Arnold diffusion conjecture for convex Hamiltonians in the smooth category in the sense of cusp-residual genericit

Complete λ\lambda-surfaces in R3\mathbb R^3

The purpose of this paper is to study complete $\lambda$-surfaces in Euclidean space $\mathbb R^3$. A complete classification for 2-dimensional complete $\lambda$-surfaces in Euclidean space $\mathbb R^3$ with constant squared norm of the second fundamental form is given.Comment: 19 pages, comments are welcom

Construction and classification of symmetry protected topological phases in interacting fermion systems

The classification and lattice model construction of symmetry protected topological (SPT) phases in interacting fermion systems are very interesting but challenging. In this paper, we give a systematic fixed point wave function construction of fermionic SPT (FSPT) states for generic fermionic symmetry group $G_f=\mathbb{Z}_2^f \times_{\omega_2} G_b$ which is a central extension of bosonic symmetry group $G_b$ (may contain time reversal symmetry) by the fermion parity symmetry group $\mathbb{Z}_2^f = \{1,P_f\}$. Our construction is based on the concept of equivalence class of finite depth fermionic symmetric local unitary (FSLU) transformations and decorating symmetry domain wall picture, subjected to certain obstructions. We will also discuss the systematical construction and classification of boundary anomalous SPT (ASPT) states which leads to a trivialization of the corresponding bulk FSPT states. Thus, we conjecture that the obstruction-free and trivialization-free constructions naturally lead to a classification of FSPT phases. Each fixed-point wave function admits an exactly solvable commuting-projector Hamiltonian. We believe that our classification scheme can be generalized to point/space group symmetry as well as continuum Lie group symmetry.Comment: 73 pages, 18 figures, 7 tables; added more examples and one more appendi

Hamiltonian Structures of KdV-Type Hierarchies and Associated W-Algebras

The $(n,m)^{\th}$ KdV hierarchy is a restriction of the KP hierarchy to a submanifold of pseudo-differential operators in a radio form. Explicit formula of the restricted Hamiltonian structure of KP is given which provides a new, more constructive proof of the isomorphism between the associated $W(n,m)$-algebra to $W_{n+m}\oplus W_m\oplus U(1)$ algebra, and the Hamiltonian property of the $(n,m)^{\th}$ KdV hierarchy as well as its Lax-Manakov triad representation. Similarly the Hamiltonian property for a version of modified $n^{\th}$ KdV and the isomorphism between $W_n$-algebra to $W_l\oplus W_m\oplus U(1)$ algebra are shown, where $l+m=n$. The role of U(1) current in both cases is also explained.Comment: 12 pages, no figure