Year: 2026
Type: preprint
Abstract: We give a rigorous one-dimensional formulation of Kane's transport proposal for probing the Euler characteristic of a Fermi sea. For a clean, translation-invariant continuum Hamiltonian with real-analytic dispersion, a Fermi sea confined to a finite momentum range, and nonzero Fermi velocity at every Fermi point, we analyze a particular Abel-regularized transport response (obtained by tracing over the Fermi sea) and prove that its large-time limit equals the Euler characteristic. We derive an explicit finite-time formula, show that quantization requires the large-time limit, and obtain a convergence rate under additional nonstationarity assumptions. We also prove the lattice analog, where the sharp commutator is trace-class and a completely filled band contributes zero. Finite-volume calculations illustrate the prescribed order of the thermodynamic and large-time limits.
Source: arXiv (Cornell University)
Authors: Hu, Yichen, Shapiro, Jacob
Institutions: Florida Atlantic University, Princeton University
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7204825018
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