Entanglement and chaos in warped conformal field theories

Various aspects of warped conformal field theories (WCFTs) are studied including entanglement entropy on excited states, the Renyi entropy after a local quench, and out-of-time-order four-point functions. Assuming a large central charge and dominance of the vacuum block in the conformal block expansion, (i) we calculate the single-interval entanglement entropy on an excited state, matching previous finite temperature results by changing the ensemble; and (ii) we show that WCFTs are maximally chaotic, a result that is compatible with the existence of black holes in the holographic duals. Finally, we relax the aforementioned assumptions and study the time evolution of the Renyi entropy after a local quench. We find that the change in the Renyi entropy is topological, vanishing at early and late times, and nonvanishing in between only for charged states in spectrally-flowed WCFTs.Comment: 31 pages; v2: corrected typos, matches published versio

The Orthogonal Expansion in Time-Domain Method for Solving Maxwell Equations Using Paralleling-in-Order Scheme

The orthogonal expansion in time-domain method is a new kind of unconditionally stable finite-difference time-domain (FDTD) method for solving the Maxwell equation efficiently. Generally, it can be implemented by two schemes: marching-on-in-order and paralleling-in-order, which, respectively, use weighted Laguerre polynomials and associated Hermite functions as temporal expansions and testing functions. This chapter summarized paralleling-in-order-based FDTD method using associated Hermite functions and Legendre polynomials. And a comparison from theoretical analysis to numerical examples is shown. The LD integral transfer matrix can be considered as a “dual” transformation for AH differential matrix, which gives a possible way to find more potential orthogonal basis function to implement a paralleling-in-order scheme. In addition, the differences with these two orthogonal functions are also analyzed. From the numerical results, we can see their agreements in some general cases while differing in some cases such as shielding analysis with the long-time response requirement

Market Stability Switches in a Continuous-Time Financial Market with Heterogeneous Beliefs

By considering a financial market of fundamentalists and trend followers in which the price trend of the trend followers is formed as a weighted average of historical prices, we establish a continuous-time financial market model with time delay and examines the impact of time delay on market price dynamics. Conditions for the stability of the fundamental price in terms of agents' behavior parameters and time delay are obtained. In particular, it is found that an increase in time delay can not only destabilize the market price but also stabilize an otherwise unstable market price, leading to stability switching as delay increases. This interesting phenomena shed new light in understanding of mechanism on the market stability. When the fundamental price becomes unstable through Hopf bifurcations, suffcient conditions on the stability and global existence of the periodic solution are obtained.asset price; fundamentalists; trend followers; delay differential equations; stability; bifurcations

Consolidation effect of visual function training on children with different degrees of amblyopia

AIM: To observe the consolidation effect of visual function training in amblyopic therapy on children with amblyopia of different degrees(mild, moderate and severe)which had been normalized. <p>METHODS: Totally 78 amblyopic children were divided into two groups: visual function training group(<i>n</i>=36, 70 eyes)and control group(<i>n</i>=42, 67 eyes). The rollback situation of the two groups in 6, 12, 24 and 36 months were observed after visual acuity reached 0.9 during treatment.<p>RESULTS: The rollback rates were both 0 in visual function training group and control group with different degrees of amblyopia after 6 months. There was no significant difference in rollback rate between the 2 groups with different degrees of amblyopia after 6 and 12 months. There was no significant difference in rollback rate between the two groups with mild amblyopia after 24 and 36 months(<i>P</i>=0.269, 0.269). However, the rollback rate in training group with moderate amblyopia was significantly different from in control group after 24 and 36 months(<i>P</i>=0.004, 0.002). There was no significant difference in rollback rate between the two groups with severe amblyopia after 24 and 36 months. <p>CONCLUSION: Visual function training can reduce the rollback rate and consolidate the effect of amblyopic treatment effectively for children with moderate amblyopia. However, the effect is not as good for children with mild and severe amblyopia

An optimized analytical method for the simultaneous detection of iodoform, iodoacetic acid, and other trihalomethanes and haloacetic acids in drinking water

An optimized method is presented using liquid-liquid extraction and derivatization for the extraction of iodoacetic acid (IAA) and other haloacetic acids (HAA9) and direct extraction of iodoform (IF) and other trihalomethanes (THM4) from drinking water, followed by detection by gas chromatography with electron capture detection (GC-ECD). A Doehlert experimental design was performed to determine the optimum conditions for the five most significant factors in the derivatization step: namely, the volume and concentration of acidic methanol (optimized values  = 15%, 1 mL), the volume and concentration of Na2SO4 solution (129 g/L, 8.5 mL), and the volume of saturated NaHCO3 solution (1 mL). Also, derivatization time and temperature were optimized by a two-variable Doehlert design, resulting in the following optimized parameters: an extraction time of 11 minutes for IF and THM4 and 14 minutes for IAA and HAA9; mass of anhydrous Na2SO4 of 4 g for IF and THM4 and 16 g for IAA and HAA9; derivatization time of 160 min and temperature at 40°C. Under optimal conditions, the optimized procedure achieves excellent linearity (R2 ranges 0.9990–0.9998), low detection limits (0.0008–0.2 µg/L), low quantification limits (0.008–0.4 µg/L), and good recovery (86.6%–106.3%). Intra- and inter-day precision were less than 8.9% and 8.8%, respectively. The method was validated by applying it to the analysis of raw, flocculated, settled, and finished waters collected from a water treatment plant in China