Holographic coherent states from random tensor networks

Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we generalize the random tensor network approach to allow quantum superposition of different spatial geometries. We set up a framework in which all possible bulk spatial geometries, characterized by weighted adjacent matrices of all possible graphs, are mapped to the boundary Hilbert space and form an overcomplete basis of the boundary. We name such an overcomplete basis as holographic coherent states. A generic boundary state can be expanded on this basis, which describes the state as a superposition of different spatial geometries in the bulk. We discuss how to define distinct classical geometries and small fluctuations around them. We show that small fluctuations around classical geometries define "code subspaces" which are mapped to the boundary Hilbert space isometrically with quantum error correction properties. In addition, we also show that the overlap between different geometries is suppressed exponentially as a function of the geometrical difference between the two geometries. The geometrical difference is measured in an area law fashion, which is a manifestation of the holographic nature of the states considered.Comment: 33 pages, 8 figures. An error corrected on page 14. Reference update

A Study on the Location Determinants of the US FDI in China

he US foreign direct investment in China plays a leading role in the process of introducing FDI to China. This paper carries on an empirical research dynamically on the location factors of US foreign direct investment in China, adopting Johansen cointegration test, the VEC model, Granger causality test and variance decomposition technology, based on analytical data in the period from 1983 to 2006. The studying result demonstrates that there is a stable relationship among the US foreign direct investment in China, China’s GDP, fixed asset investment in China and the prophase stock of the US foreign direct investment in the long-run. And China’s GDP is the major power to induce the US FDI to bias the long-term equilibrium