Black Hole Radiation with Modified Dispersion Relation in Tunneling Paradigm: Free-fall Frame

Due to the exponential high gravitational red shift near the event horizon of a black hole, it might appear that the Hawking radiation would be highly sensitive to some unknown high energy physics. To study effects of any unknown physics at the Planck scale on the Hawking radiation, the dispersive field theory models have been proposed, which are variations of Unruh's sonic black hole analogy. In this paper, we use the Hamilton-Jacobi method to investigate the dispersive field theory models. The preferred frame is the free-fall frame of the black hole. The dispersion relation adopted agrees with the relativistic one at low energy but is modified near the Planck mass $m_{p}$. The corrections to the Hawking temperature are calculated for massive and charged particles to $\mathcal{O}\left( m_{p}^{-2}\right)$ and neutral and massless particles with $\lambda=0$ to all orders. The Hawking temperature of radiation agrees with the standard one at the leading order. After the spectrum of radiation near the horizon is obtained, we use the brick wall model to compute the thermal entropy of a massless scalar field near the horizon of a 4D spherically symmetric black hole and a 2D one. Finally, the luminosity of a Schwarzschild black hole is calculated by using the geometric optics approximation.Comment: 28 pages. arXiv admin note: substantial text overlap with arXiv:1505.0304

Character of frustration on magnetic correlation in doped Hubbard model

The magnetic correlation in the Hubbard model on a two-dimensional anisotropic triangular lattice is studied by using the determinant quantum Monte Carlo method. Around half filling, it is found that the increasing frustration $t'/t$ could change the wave vector of maximum spin correlation along ($\pi,\pi$)$\rightarrow$($\pi,\frac{5\pi}{6}$)$\rightarrow$($\frac{5\pi}{6},\frac{5\pi}{6}$)$\rightarrow$ ($\frac{2\pi}{3},\frac{2\pi}{3}$), indicating the frustration's remarkable effect on the magnetism. In the studied filling region =1.0-1.3, the doping behaves like some kinds of {\it{frustration}}, which destroys the $(\pi,\pi)$ AFM correlation quickly and push the magnetic order to a wide range of the $(\frac{2\pi}{3},\frac{2\pi}{3})$ $120^{\circ}$ order when the $t'/t$ is large enough. Our non-perturbative calculations reveal a rich magnetic phase diagram over both the frustration and electron doping.Comment: 6 pages, 7 figure

Multiagent Bidirectionally-Coordinated Nets: Emergence of Human-level Coordination in Learning to Play StarCraft Combat Games

Many artificial intelligence (AI) applications often require multiple intelligent agents to work in a collaborative effort. Efficient learning for intra-agent communication and coordination is an indispensable step towards general AI. In this paper, we take StarCraft combat game as a case study, where the task is to coordinate multiple agents as a team to defeat their enemies. To maintain a scalable yet effective communication protocol, we introduce a Multiagent Bidirectionally-Coordinated Network (BiCNet ['bIknet]) with a vectorised extension of actor-critic formulation. We show that BiCNet can handle different types of combats with arbitrary numbers of AI agents for both sides. Our analysis demonstrates that without any supervisions such as human demonstrations or labelled data, BiCNet could learn various types of advanced coordination strategies that have been commonly used by experienced game players. In our experiments, we evaluate our approach against multiple baselines under different scenarios; it shows state-of-the-art performance, and possesses potential values for large-scale real-world applications.Comment: 10 pages, 10 figures. Previously as title: "Multiagent Bidirectionally-Coordinated Nets for Learning to Play StarCraft Combat Games", Mar 201