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cond-mat.mes-hall2026
The Hodge structure of Berry-phase transport: topology, geometry, and noise
Zhi-Wei Wang, Samuel L. Braunstein
We show that the Hodge-de Rham decomposition of the Berry curvature organises the transport of a Bloch band and its fluctuations within a single geometric structure. Splitting the…
cond-mat.mes-hall2026
Hodge Topology of Semiclassical Transport: A Coordinate-Free Geometric Framework for the Anomalous Hall Effect and Non-Linear Berry Dipole
Zhi-Wei Wang, Samuel L. Braunstein
We establish a coordinate-free differential geometric framework for anomalous transport in topological bands using the Hodge-de Rham decomposition of the Brillouin zone. Standard f…