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

SU(3) trimer resonating-valence-bond state on the square lattice

We propose and study an SU(3) trimer resonating-valence-bond (tRVB) state with $C_{4v}$ point-group symmetry on the square lattice. By devising a projected entangled-pair state representation, we show that all (connected) correlation functions between local operators in this SU(3) tRVB state decay exponentially, indicating its gapped nature. We further calculate the modular $S$ and $T$ matrices by constructing all nine topological sectors on a torus and establish the existence of $\mathbb{Z}_3$ topological order in this SU(3) tRVB state.Comment: 6 pages, 6 figure

Scale invariant distribution functions in quantum systems with few degrees of freedom

Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time. Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables. At equilibrium these functions decay over a typical scale set by the temperature, but they can become scale invariant in a sudden quantum quench. We exemplify this effect through the analysis of linear and non-linear quantum oscillators. We find that their distribution functions generically diverge logarithmically close to the stable points of the classical dynamics. Our study opens the possibility to address integrability and its breaking in distribution functions, with immediate applications to matter-wave interferometers.Comment: 8+10 pages. Scipost Submissio

Carabus (Coleoptera: Carabidae) assemblages of native forests and non-native plantations in Northern China

The effects of non-native plantation established after clear-cutting were studied in Dongling Mountain region, Northern China. Pitfall catches of Carabus beetles from a non-native larch plantation were compared with those from two native forests, an oak forest and a mixed broad-leaved forest. More individuals were captured from the mixed broad-leaved forest and the larch plantation than from the oak forest. For the threemost abundant species in this area, C. crassesculptus peaked in abundance in the mixed broad-leaved forest; C. manifestus peaked in the larch plantation, and C. sculptipennis in the oak forest. Measured by PcoAusing Bray-Curtis index of dissimilarity, species composition of the larch plantation was different from the two native forests, but overlapped remarkably with them. All the three abundant species showed a similar positive relationship between local distribution and abundance. Captures of abundant species were clumped within the forest, but the extent of aggregation among forests was different. Monthly catches of total Carabus, and C. crassesculptus alone, peaked in June–August in all the three forests, but C. manifestus peaked in June and again in August. Our results suggest that the planting of non-native larch does not have a detrimental effect on Carabus assemblages in general, but it changes the spatial distribution and abundance compared to the native forests

Habitat associations and seasonal activity of carabid beetles (Coleoptera: Carabidae) in Dongling Mountain, North China

Habitat distribution and seasonal occurrence of carabid beetles were determined using pitfall traps in 1999 and 2000 in the temperate forest zone of the Dongling Mountain, North China. Eight sites differing in vegetation and moisture were selected so as to represent four habitat types. Carabid assemblages of the six forested habitats (lowland, upland and coppice) weremore similar to each other than to the two shrub assemblages. Lowland forest had the highest species richness, and coppice forest had the highest diversity (H’) and equitability (J). Of the 41 species caught, the 18 most abundant species were divided into four distribution types: habitat generalists, forest generalists, forest specialists, and shrub (or coppice) specialists. Mean catches of all beetles showed clear peaks from May to August in nearly all habitats. The catches of the six most abundant species were more or less positively correlated during the two study years, suggesting their similar habitat preferences