On the definition of entanglement entropy in lattice gauge theories

We focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contains gauge non-invariant states as well. Working in the extended Hilbert space, we can define entanglement entropy associated with an arbitrary subset of links, not only for abelian but also for non-abelian theories. We then derive the associated replica formula. We also discuss the issue of gauge invariance of the entanglement entropy. In the $Z_N$ gauge theories in arbitrary space dimensions, we show that all the standard properties of the entanglement entropy, e.g. the strong subadditivity, hold in our definition. We study the entanglement entropy for special states, including the topological states for the $Z_N$ gauge theories in arbitrary dimensions. We discuss relations of our definition to other proposals.Comment: 29 pages, 1 figure, a comment and more references added, some typos correcte

Prediction of Electric Field Strength at 10m Distance Using Emission Source Finding Method

The equipment under test (EUT) was modeled by current sources. The current positions were estimated using the finding method of radiated emission source by electric field strength data alone. The current vectors were determined by the conditions, where Norm (deviation between the calculated electric field and the measured one) was minimized. Using estimated current sources model, the electric filed strength at 10m distance was predicted. The predicted results were compared with the measured data for an imitated equipment and a personal computer. The results indicate that the radiation patterns were similar to the measured ones, and the maximum electric field strength at10m distance was comparable to the measured value and the calculated value on the assumption where electric field decreases in proportion to distance.2004 International Symposium on Electromagnetic Compatibility (EMC\u2704/Sendai), June 1-4, 2004, Sendai International Center, Sendai, Japa