Four-fold non-Hermitian phase transitions and non-reciprocal coupled resonator optical waveguides

Non-Hermitian systems can exhibit extraordinary sensitivity to boundary conditions. Given that topological boundary modes and non-Hermitian skin effects can either coexist or individually appear in non-Hermitian systems, it is of great value to present a comprehensive non-Hermitian phase diagram, for further flexible control in realistic non-Hermitian systems. Here, we reveal four-fold non-Hermitian phase transitions at a mathematically level, where phase I exhibits only topological boundary modes, phase II displays both topological boundary modes and skin modes, phase III exhibits only skin modes, and phase IV cannot manifest any boundary modes. By deriving non-Hermitian winding numbers, the existence or non-existence condition of topological boundary modes are analytically expressed, consistent with the numerical results obtained through the iterative Green's function method. Combining with the study on non-Hermitian skin effects, we rigorously establish the four-fold phase diagram. We also design an array of coupled resonator optical waveguides. The introduction of non-Hermiticity in the photonic structure induces a phenomenon similar to band inversion in topological insulators, indicating the presence of topological boundary modes in the photonic bands.Comment: 11 pages, 6 figure

Decoding Social Sentiment in DAO: A Comparative Analysis of Blockchain Governance Communities

Blockchain technology is leading a revolutionary transformation across diverse industries, with effective governance standing as a critical determinant for the success and sustainability of blockchain projects. Community forums, pivotal in engaging decentralized autonomous organizations (DAOs), wield a substantial impact on blockchain governance decisions. Concurrently, Natural Language Processing (NLP), particularly sentiment analysis, provides powerful insights from textual data. While prior research has explored the potential of NLP tools in social media sentiment analysis, a gap persists in understanding the sentiment landscape of blockchain governance communities. The evolving discourse and sentiment dynamics on the forums of top DAOs remain largely unknown. This paper delves deep into the evolving discourse and sentiment dynamics on the public forums of leading DeFi projects -- Aave, Uniswap, Curve Dao, Aragon, Yearn.finance, Merit Circle, and Balancer -- placing a primary focus on discussions related to governance issues. Despite differing activity patterns, participants across these decentralized communities consistently express positive sentiments in their Discord discussions, indicating optimism towards governance decisions. Additionally, our research suggests a potential interplay between discussion intensity and sentiment dynamics, indicating that higher discussion volumes may contribute to more stable and positive emotions. The insights gained from this study are valuable for decision-makers in blockchain governance, underscoring the pivotal role of sentiment analysis in interpreting community emotions and its evolving impact on the landscape of blockchain governance. This research significantly contributes to the interdisciplinary exploration of the intersection of blockchain and society, with a specific emphasis on the decentralized blockchain governance ecosystem