Perturbative BV-BFV formalism with homotopic renormalization: a case study

We report a rigorous quantization of topological quantum mechanics on $\mathbb{R}_{\geqslant 0}$ and $\mathbf{I}= [0, 1]$ in perturbative BV-BFV formalism. Costello's homotopic renormalization is extended, and incorporated in our construction. Moreover, BV quantization of the same model studied in our previous work is derived from the BV-BFV quantization, leading to a comparison between different interpretations of ''state'' in these two frameworks.Comment: 31 pages, 2 figures. Added some reference

Analysis of spatial and temporal variations of NDVI and its driving factors in the corridor of Lan-Xin railway

Introduction: Vegetation is the main factor of ecological stability, but the construction of largescale corridor projects will bring some damage to vegetation.Methods: Based on the NDVI, temperature and precipitation data of the growing season from 1990–2021 (June to September), this paper uses the maximum synthesis method, trend analysis method, correlation analysis method and coefficient of variation method to study the spatial-temporal changes and driving factors of NDVI in the past 32 years, taking the 30 km belt buffer zone along the Lan-Xin Railway as the research area. The influence range of railway construction on NDVI in different climatic conditions is analyzed.Results: The results showed that: (1) From 1990–2021, the average annual temperature of the growing season in the study area showed an increasing trend, the average annual precipitation showed a decreasing trend, and the average annual NDVI showed an increasing trend; NDVI was positively correlated with temperature in 54.04%, and positively correlated with precipitation in 62.88%. Precipitation had a greater effect on NDVI than temperature. (2) Under the same climatic conditions, the NDVI variability coefficient in the study area fluctuates significantly within 3,000–21,000 m along the railway line, stabilizing beyond 21,000 m; the impact range of railway construction on NDVI gradually increases with increasing precipitation within the same temperature range, and increases gradually with rising temperatures within the same precipitation range. (3) During the growing season (June to September) in the study area, when the temperature is below 25°C, NDVI increases initially with increasing precipitation before decreasing, showing an overall upward trend; when the temperature is above 25°C, NDVI initially increases with increasing precipitation before decreasing. High temperature and high precipitation will inhibit vegetation growth and reduce NDVI. The NDVI of the core area before the railway construction is larger than that of the background area, while the NDVI of the core area after the railway construction is smaller than that of the background area.Discussion: In short, the construction of Lan-Xin Railway has a certain influence on NDVI along the line. When studying the impact of large-scale engineering projects on vegetation in the future, higher resolution imagery can be used along with the incorporation of human activities' influence. These factors will enable more accurate and comprehensive research

Preservation of Topological Surface States in Millimeter-Scale Transferred Membranes

Ultrathin topological insulator membranes are building blocks of exotic quantum matter. However, traditional epitaxy of these materials does not facilitate stacking in arbitrary orders, while mechanical exfoliation from bulk crystals is also challenging due to the non-negligible interlayer coupling therein. Here we liberate millimeter-scale films of the topological insulator Bi2Se3, grown by molecular beam epitaxy, down to 3 quintuple layers. We characterize the preservation of the topological surface states and quantum well states in transferred Bi2Se3 films using angle-resolved photoemission spectroscopy. Leveraging the photon-energy-dependent surface sensitivity, the photoemission spectra taken with 6 and 21.2 eV photons reveal a transfer-induced migration of the topological surface states from the top to the inner layers. By establishing clear electronic structures of the transferred films and unveiling the wave function relocation of the topological surface states, our work lays the physics foundation crucial for the future fabrication of artificially stacked topological materials with single-layer precision