Schrödinger evolution of two-dimensional black holes

This paper systematically treats the evolving quantum state for two-dimensional black holes, with particular focus on the CGHS model, but also elucidating features generalizing to higher dimensions. This is done in Schrödinger picture(s), to exhibit the dynamic evolution of the state at intermediate times. After a review of classical solutions, also connecting to descriptions of higher-dimensional black holes, it overviews the canonical quantum treatment of the full evolution, including gravitational dynamics. Derived in an approximation to this, following conversion to “perturbation picture”, is the evolution of the quantum matter on the background geometry. Features of the evolving matter state are described, based on choice of a time slicing to put the evolution into ADM form. The choices of slicing as well as coordinates on the slices result in different quantum “pictures” for treating the evolution. If such a description is based on smooth trans-horizon slices, that avoids explicit reference to ultra-planckian modes familiar from traditional treatments, and exhibits the Hawking excitations as emerging from a “quantum atmosphere” with thickness comparable to the inverse temperature. Detailed study of the state exhibits the entanglement structure between Hawking quanta and the partner excitations inside the black hole, and the corresponding “missing information”. This explicit description also allows direct study of the evolution and features, e.g. as seen by infalling observers, of these partner excitations, helping to address various puzzles with them. Explicit treatment of the evolving state, and its extension to higher dimensions, provides further connections to information theory and a starting point for study of corrections that can unitarize evolution, arising from new quantum gravity effects — whether wormholes or something entirely different.

Temporal evolution of tagging subnetwork features and motif under different activity levels – take the Q&A community Zhihu as an example

Purpose This paper aims to study the characteristics and evolution rules of tagging knowledge network for users with different activity levels in question-and-answer (Q&A) community represented by Zhihu. Design/methodology/approach A random sample of issue tag data generated by topics in the Zhihu network environment is selected. By defining user quality and selecting the top 20% and bottom 20% of users to focus on, i.e. top users and bot users, the authors apply time slicing for both types of data to construct label knowledge networks, use Q-Q diagrams and ARIMA models to analyze network indicators and introduce the theory and methods of network motif. Findings This study shows that when the power index of degree distribution is less than or equal to 3.1, the ARIMA model with rank index of label network has a higher fitting degree. With the development of the community, the correlation between tags in the tagging knowledge network is very weak. Research limitations/implications It is not comprehensive and sufficient to classify users only according to their activity levels. And traditional statistical analysis is not applicable to large data sets. In the follow-up work, the authors will further explore the characteristics of the network at a larger scale and longer timescale and consider adding more node features, including some edge features. Then, users are statistically classified according to the attributes of nodes and edges to construct complex networks, and algorithms such as machine learning and deep learning are used to calculate large-scale data sets to deeply study the evolution of knowledge networks. Practical implications This paper uses the real data of the Zhihu community to divide users according to user activity and combines the theoretical methods of statistical testing, time series and network motifs to carry out the time series evolution of the knowledge network of the Q&A community. And these research methods provide other network problems with some new ideas. Research has found that user activity has a certain impact on the evolution of the tagging network. The tagging network followed by users with high activity level tends to be stable, and the tagging network followed by users with low activity level gradually fluctuates. Social implications Research has found that user activity has a certain impact on the evolution of the tagging network. The tagging network followed by users with high activity level tends to be stable, and the tagging network followed by users with low activity level gradually fluctuates. For the community, understanding the formation mechanism of its network structure and key nodes in the network is conducive to improving the knowledge system of the content, finding user behavior preferences and improving user experience. Future research work will focus on identifying outbreak points from a large number of topics, predicting topical trends and conducting timely public opinion guidance and control. Originality/value In terms of data selection, the user quality is defined; the Zhihu tags are divided into two categories for time slicing; and network indicators and network motifs are compared and analyzed. In addition, statistical tests, time series analysis and network modality theory are used to analyze the tags.