Large-N scaling behavior of the quantum fisher information in the Dicke model

Quantum Fisher information (QFI) of the reduced two-atom state is employed to capture the quantum criticality of the superradiant phase transition in the Dicke model in the infinite size and finite-$N$ systems respectively. The analytical expression of the QFI of its ground state is evaluated explicitly. And finite-size scaling analysis is performed with the large accessible system size due to the effective bosonic coherent-state technique. We also investigate the large-size scaling behavior of the scaled QFI of the reduced $N$-atom state and show the accurate exponent.Comment: 6pages,2figure

Searching For a Lost Plane

Malaysia plane MH370 disappeared en route from Kuala Lumpur to Beijing on 8, March 2014. Besides considering the factors such as air piracy, weather, electromagnetic wave, and kinds of bugs of the airplane, in order to find the wreckage efficiently the growing concern is to confirm a limited area where the airplane probably fell, and then to find an optimum way to find the plane. It’s essential to build such a model involving both of the two layers mentioned above that can cover all the searching area by using the most efficient way. The first layer is to confirm the limited area. We use the Poisson Probability Distribution, the Drag equation, and the Proper Orthogonal Decomposition Theorem to assume the direction of the airplane and the sea area where it probably fell. All assumptions are based on the actual situation. The second model will basically rely on the Bayesian principles. In this case, the model would be advantageous as it will rely on contingency as an important role in the search for lost objects in the sea or on land. As matter of fact, any information that is provided to the search team would be put into good use as it will be used in developing the probabilities. It is also good in that it\u27s flexible and would be good enough to sustain the ongoing search even with new information or facts obtained regarding the flight of the plane and/or the initial findings of the debris. This helps in rounding down to a lesser geographical search region and, by extension, increases the probability of getting the plane

Further results on the nullity of signed graphs

The nullity of a graph is the multiplicity of the eigenvalues zero in its spectrum. A signed graph is a graph with a sign attached to each of its edges. In this paper, we obtain the coefficient theorem of the characteristic polynomial of a signed graph, give two formulae on the nullity of signed graphs with cut-points. As applications of the above results, we investigate the nullity of the bicyclic signed graph $\Gamma(\infty(p,q,l))$, obtain the nullity set of unbalanced bicyclic signed graphs, and thus determine the nullity set of bicyclic signed graphs.Comment: 17 pages. arXiv admin note: text overlap with arXiv:1207.6765, arXiv:1107.0400 by other author

The entanglement dynamics of interacting qubits embedded in a spin environment with Dzyaloshinsky-Moriya term

We investigate the entanglement dynamics of two interacting qubits in a spin environment, which is described by an XY model with Dzyaloshinsky-Moriya (DM) interaction. The competing effects of environmental noise and interqubit coupling on entanglement generation for various system parameters are studied. We find that the entanglement generation is suppressed remarkably in weak-coupling region at quantum critical point (QCP). However, the suppression of the entanglement generation at QCP can be compensated both by increasing the DM interaction and by decreasing the anisotropy of the spin chain. Beyond the weak-coupling region, there exist resonance peaks of concurrence when the system-bath coupling equals to external magnetic field. We attribute the presence of resonance peaks to the flat band of the self-Hamiltonian. These peaks are highly sensitive to anisotropy parameter and DM interaction.Comment: 8 pages, 9 figure