2023/04/24 by R. Merlin, Merlin, R.
Physics and Astronomy · #Advanced Chemical Physics Studies #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2304.12215
openalex publication_date 2023/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The concept of Wannier-Stark ladders, describing the equally spaced spectrum of a tightly-bound particle in a constant electric field, is generalized to account for arbitrary slowly-varying potentials. It is shown that an abrupt transition exists that separates Wannier-Stark-like from effective-mass-like behavior when the depth of the perturbation becomes equal to the width of the band of extended states. For potentials bounded from below, the spectrum bifurcates above the critical energy while the wavefunctions detach from the effective-mass region and split into two pieces.