We report ^{75}As NMR measurements on the new quasi-one-dimensional superconductor K_{2}Cr_{3}As_{3} (T_{c}∼6.1  K) [J. K. Bao et al., Phys. Rev. X 5, 011013 (2015)]. We found evidence for strong enhancement of Cr spin fluctuations above T_{c} in the [Cr_{3}As_{3}]_{∞} double-walled subnanotubes based on the nuclear spin-lattice relaxation rate 1/T_{1}. The power-law temperature dependence, 1/T_{1}T∼T^{-γ} (γ∼0.25), is consistent with the Tomonaga-Luttinger liquid. Moreover, absence of the Hebel-Slichter coherence peak of 1/T_{1} just below T_{c} suggests an unconventional nature of superconductivity.

We report 133 Cs NMR and 75 As Nuclear Quadrupole Resonance (NQR) measurements on the normal metallic state above Tc of a quasi-one-dimensional superconductor Cs2Cr3As3 (Tc < 1.6 K). From the 133 Cs NMR Knight shift 133 K measured at the Cs1 site, we show that the uniform spin susceptibility χspin increases from 295 K to ∼ 60 K, followed by a mild suppression; χspin then levels off below ∼10 K. In contrast, a vanishingly small magnitude of 133 K indicates that Cs2 sites contribute very little to electrical conduction and the exchange interactions between 3d electrons at Cr sites. Low frequency Cr spin dynamics, reflected on 75 As 1/T1T (the nuclear spin-lattice relaxation rate 1/T1 divided by temperature T ), shows an analogous trend as χspin. Comparison with the results of 1/T1T near Tc with K2Cr3As3 (Tc = 6.1 K) and Rb2Cr3As3 (Tc = 4.8 K) establishes a systematic trend that substitution of K + ions with larger alkali ions progressively suppresses Cr spin fluctuations together with Tc.

By incorporating ecological dynamics into evolutionary games, we introduce natural and unnatural death to the spatial prisoner's dilemma game in which individuals can play mixed strategies. This introduction can give a simple explanation for the emergence and abundance of cooperation in animal and human societies. We found that individuals are more likely to cooperate in a highly competitive environment. In addition, our simulation results suggest that the individuals would tend to cooperate when the temptation to defect is small.

Dark energy phenomena has inspired lots of investigations on the cosmological constant problems. In order to understand its origin and properties as well as its impacts on universe's evolutions, there are many approaches to modify the well-known General Relativity, such as the Weyl-Lyra Geometry. In the well studied cosmology model within Lyra geometry, there is a problem that the first law of thermodynamics is violated. To unravel this issue, if we use the effective density and pressure in the Lyra cosmology model to preserve the first law of thermodynamics in the cosmos, the former 1-form (β, 0, 0, 0) cannot give a proper vacuum behavior. In this paper, the auxiliary 1-form is modified to overcome this difficulty. It can be shown that the complex terms in the field equation derived from the regime of Lyra Geometric 3 2 φ µ φν − 3 4 δ µ ν φ α φαwith our new 1-form could behave just as the cosmological constant. This work can be regarded as a new exploration on a possible origin of the cosmological constant from a Lyra cosmology model. PACS numbers :98.80.-k 98.80.Qc

Lyra geometry is a conformal geometry originated from Weyl geometry. In this article, we derive the exterior field equation under spherically symmetric gauge function x 0 (r) and metric in Lyra geometry. When we impose a specific form of the gauge function x 0 (r), the radial differential equation of the metric component g 00 will possess an irregular singular point(ISP) at r = 0.Moreover, we apply the method of dominant balance and then get the asymptotic behavior of the new spacetime solution. The significance of this work is that we could use a series of smooth gauge functions x 0 (r) to modulate the degree of divergence of the singularity at r = 0 and the singularity will become a naked singularity under certain conditions. Furthermore, we investigate the physical meaning of this novel behavior of spacetime in Lyra geometry and find out that no spaceship with finite integrated acceleration could arrive at this singularity at r = 0. The physical meaning of gauge function and integrability is also discussed.