2026-10-26 · arXiv Quantum Physics
arXiv:2610.32710v1 Announce Type: cross
Abstract: We extend the discrete WKB method to one-dimensional bipartite tight-binding chains of free fermions with slowly varying hopping amplitudes and on-site potentials. We focus on the inhomogeneous Rice-Mele model, suggesting possible experimental realizations thereof in optical superlattices. We derive explicit semiclassical expressions for the single-particle wave functions and density of states, as well as the sublattice-resolved local particle densities and filling fraction at arbitrary Fermi energy. In particular, we show that the WKB density profiles agree with those obtained from the local-density approximation. We analyze the spatial dependence of the local band edges and its consequences for the global spectral structure, and clarify the role played by the phase-space topology in determining the Bohr-Sommerfeld quantization conditions. Finally, we illustrate our results with two representative examples: a homogeneous Rice-Mele chain subject to a harmonic trap and a fully inhomogeneous chain containing a domain wall.
原文链接：https://arxiv.org/abs/2610.32710
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