Exact Cosmological Solutions of f(R)f(R) Theories via Hojman Symmetry

Nowadays, $f(R)$ theory has been one of the leading modified gravity theories to explain the current accelerated expansion of the universe, without invoking dark energy. It is of interest to find the exact cosmological solutions of $f(R)$ theories. Besides other methods, symmetry has been proved as a powerful tool to find exact solutions. On the other hand, symmetry might hint the deep physical structure of a theory, and hence considering symmetry is also well motivated. As is well known, Noether symmetry has been extensively used in physics. Recently, the so-called Hojman symmetry was also considered in the literature. Hojman symmetry directly deals with the equations of motion, rather than Lagrangian or Hamiltonian, unlike Noether symmetry. In this work, we consider Hojman symmetry in $f(R)$ theories in both the metric and Palatini formalisms, and find the corresponding exact cosmological solutions of $f(R)$ theories via Hojman symmetry. There exist some new solutions significantly different from the ones obtained by using Noether symmetry in $f(R)$ theories. To our knowledge, they also have not been found previously in the literature. This work confirms that Hojman symmetry can bring new features to cosmology and gravity theories.Comment: 16 pages, revtex4; v2: discussions added, Nucl. Phys. B in press; v3: published version. arXiv admin note: text overlap with arXiv:1505.0754

Criticality in Translation-Invariant Parafermion Chains

In this work we numerically study critical phases in translation-invariant $\mathbb{Z}_N$ parafermion chains with both nearest- and next-nearest-neighbor hopping terms. The model can be mapped to a $\mathbb{Z}_N$ spin model with nearest-neighbor couplings via a generalized Jordan-Wigner transformation and translation invariance ensures that the spin model is always self-dual. We first study the low-energy spectrum of chains with only nearest-neighbor coupling, which are mapped onto standard self-dual $\mathbb{Z}_N$ clock models. For $3\leq N\leq 6$ we match the numerical results to the known conformal field theory(CFT) identification. We then analyze in detail the phase diagram of a $N=3$ chain with both nearest and next-nearest neighbor hopping and six critical phases with central charges being $4/5$, 1 or 2 are found. We find continuous phase transitions between $c=1$ and $c=2$ phases, while the phase transition between $c=4/5$ and $c=1$ is conjectured to be of Kosterlitz-Thouless type.Comment: published versio

Damage detection of gusset plate condtion in truss bridges based on wavelet packet energy percentage

This paper investigates the possibility and effectiveness of using a recently developed relative displacement sensor for the damage detection of gusset plate conditions in steel truss bridges. The developed sensor is an innovative design offering some advantages and unique features, and is a much easier and cheaper method of structural health monitoring due to the simplicity of its direct measurement of relative displacement without the need for a stable reference point. To investigate the potential applications of the developed sensor to the damage detection of joint conditions, a steel truss bridge model is fabricated in the laboratory and installed with the developed sensors to detect the loosen bolt damage in the gusset plates by using measured relative displacements. Those measured relative displacement measurements from the free vibration tests of both the undamaged and damaged truss models are analyzed, and a damage index based on the wavelet packet energy percentage change is used to detect the existence of the loosen bolt damage in steel truss bridges. Experimental studies demonstrate that the developed relative displacement sensor has a sensitive performance to indicate the joint conditions in steel truss bridges

Hexagon-singlet solid ansatz for the spin-1 kagome antiferromagnet

We perform a systematic investigation on the hexagon-singlet solid (HSS) states, which are a class of spin liquid candidates for the spin-1 kagome antiferromagnet. With the Schwinger boson representation, we show that all HSS states have exponentially decaying correlations and can be interpreted as a (special) subset of the resonating Affleck-Kennedy-Lieb-Tasaki (AKLT) loop states. We provide a compact tensor network representation of the HSS states, with which we are able to calculate physical observables efficiently. We find that the HSS states have vanishing topological entanglement entropy, suggesting the absence of intrinsic topological order. We also employ the HSS states to perform a variational study of the spin-1 kagome Heisenberg antiferromagnetic model. When we use a restricted HSS ansatz preserving lattice symmetry, the best variational energy per site is found to be $e_0 = -1.3600$. In contrast, when allowing lattice symmetry breaking, we find a trimerized simplex valence bond crystal with a lower energy, $e_0=-1.3871$.Comment: 14 pages, 12 figures, published versio

Analysis on Heavy Quarkonia Transitions with Pion Emission in Terms of the QCD Multipole Expansion and Determination of Mass Spectra of Hybrids

One of the most important tasks in high energy physics is search for the exotic states, such as glueball, hybrid and multi-quark states. The transitions $\psi(ns)\to \psi(ms)+\pi\pi$ and $\Upsilon(ns)\to \Upsilon(ms)+\pi\pi$ attract great attentions because they may reveal characteristics of hybrids. In this work, we analyze those transition modes in terms of the theoretical framework established by Yan and Kuang. It is interesting to notice that the intermediate states between the two gluon-emissions are hybrids, therefore by fitting the data, we are able to determine the mass spectra of hybrids. The ground hybrid states are predicted as 4.23 GeV (for charmonium) and 10.79 GeV (for bottonium) which do not correspond to any states measured in recent experiments, thus it may imply that very possibly, hybrids mix with regular quarkonia to constitute physical states. Comprehensive comparisons of the potentials for hybrids whose parameters are obtained in this scenario with the lattice results are presented.Comment: 16 pages, 2 figur

Discovery and Identification of W' and Z' in SU(2) x SU(2) x U(1) Models at the LHC

We explore the discovery potential of W' and Z' boson searches for various SU(2) x SU(2) x U(1) models at the Large Hadron Collider (LHC), after taking into account the constraints from low energy precision measurements and direct searches at both the Tevatron (1.96 TeV) and the LHC (7 TeV). In such models, the W' and Z' bosons emerge after the electroweak symmetry is spontaneously broken. Two patterns of the symmetry breaking are considered in this work: one is SU(2)_L x SU(2)_2 x U(1)_X to SU(2)_L x U(1)_Y (BP-I), another is SU(2)_1 x SU(2)_2 x U(1)_Y to SU(2)_L x U(1)_Y (BP-II). Examining the single production channel of W' and Z' with their subsequent leptonic decays, we find that the probability of detecting W' and Z' bosons in the considered models at the LHC (with 14 TeV) is highly limited by the low energy precision data constraints. We show that observing Z' alone, without seeing a W', does not rule out new physics models with non-Abelian gauge extension, such as the phobic models in BP-I. Models in BP-II would predict the discovery of degenerate W' and Z' bosons at the LHC.Comment: 29 pages, including 11 figures, 3 tables, added references for introductio