A New Exponential Gravity

We propose a new exponential f(R) gravity model with f(R)=(R-\lambda c)e^{\lambda(c/R)^n} and n>3, \lambda\geq 1, c>0 to explain late-time acceleration of the universe. At the high curvature region, the model behaves like the \LambdaCDM model. In the asymptotic future, it reaches a stable de-Sitter spacetime. It is a cosmologically viable model and can evade the local gravity constraints easily. This model share many features with other f(R) dark energy models like Hu-Sawicki model and Exponential gravity model. In it the dark energy equation of state is of an oscillating form and can cross phantom divide line \omega_{de}=-1. In particular, in the parameter range 3< n\leq 4, \lambda \sim 1, the model is most distinguishable from other models. For instance, when n=4, \lambda=1, the dark energy equation of state will cross -1 in the earlier future and has a stronger oscillating form than the other models, the dark energy density in asymptotical future is smaller than the one in the high curvature region. This new model can evade the local gravity tests easily when n>3 and \lambda>1.Comment: 12 pages, 8 figure

Fast Algorithms at Low Temperatures via Markov Chains

For spin systems, such as the hard-core model on independent sets weighted by fugacity lambda>0, efficient algorithms for the associated approximate counting/sampling problems typically apply in the high-temperature region, corresponding to low fugacity. Recent work of Jenssen, Keevash and Perkins (2019) yields an FPTAS for approximating the partition function (and an efficient sampling algorithm) on bounded-degree (bipartite) expander graphs for the hard-core model at sufficiently high fugacity, and also the ferromagnetic Potts model at sufficiently low temperatures. Their method is based on using the cluster expansion to obtain a complex zero-free region for the partition function of a polymer model, and then approximating this partition function using the polynomial interpolation method of Barvinok. We present a simple discrete-time Markov chain for abstract polymer models, and present an elementary proof of rapid mixing of this new chain under sufficient decay of the polymer weights. Applying these general polymer results to the hard-core and ferromagnetic Potts models on bounded-degree (bipartite) expander graphs yields fast algorithms with running time O(n log n) for the Potts model and O(n^2 log n) for the hard-core model, in contrast to typical running times of n^{O(log Delta)} for algorithms based on Barvinok\u27s polynomial interpolation method on graphs of maximum degree Delta. In addition, our approach via our polymer model Markov chain is conceptually simpler as it circumvents the zero-free analysis and the generalization to complex parameters. Finally, we combine our results for the hard-core and ferromagnetic Potts models with standard Markov chain comparison tools to obtain polynomial mixing time for the usual spin system Glauber dynamics restricted to even and odd or "red" dominant portions of the respective state spaces

Very large magnetoresistance in Fe0.28_{0.28}TaS2_{2} single crystals

Magnetic moments intercalated into layered transition metal dichalcogenides are an excellent system for investigating the rich physics associated with magnetic ordering in a strongly anisotropic, strong spin-orbit coupling environment. We examine electronic transport and magnetization in Fe$_{0.28}$TaS$_{2}$, a highly anisotropic ferromagnet with a Curie temperature $T_{\mathrm{C}} \sim 68.8~$K. We find anomalous Hall data confirming a dominance of spin-orbit coupling in the magnetotransport properties of this material, and a remarkably large field-perpendicular-to-plane MR exceeding 60% at 2 K, much larger than the typical MR for bulk metals, and comparable to state-of-the-art GMR in thin film heterostructures, and smaller only than CMR in Mn perovskites or high mobility semiconductors. Even within the Fe$_x$TaS$_2$ series, for the current $x$ = 0.28 single crystals the MR is nearly $100\times$ higher than that found previously in the commensurate compound Fe$_{0.25}$TaS$_{2}$. After considering alternatives, we argue that the large MR arises from spin disorder scattering in the strong spin-orbit coupling environment, and suggest that this can be a design principle for materials with large MR.Comment: 8 pages, 8 figures, accepted in PR

Rotating non-Kerr black hole and energy extraction

The properties of the ergosphere and energy extraction by Penrose process in a rotating non-Kerr black hole are investigated. It is shown that the ergosphere is sensitive to the deformation parameter $\epsilon$ and the shape of the ergosphere becomes thick with increase of the parameter $\epsilon$. It is of interest to note that, comparing with the Kerr black hole, the deformation parameter $\epsilon$ can enhance the maximum efficiency of the energy extraction process greatly. Especially, for the case of $a>M$, the non-Kerr metric describes a superspinning compact object and the maximum efficiency can exceed 60%, while it is only 20.7% for the extremal Kerr black hole.Comment: 16 pages, 5 figures, and 2 table