2000/05/10 by Pavel Exner, V. A. Geyler, Vladimir A. Geyler · 9 citations
Mathematics · Physics and Astronomy · #Bound state #Condensed matter physics #Eigenvalues and eigenvectors #Geometric phase #Geometry #Homogeneous #Magnetic field #Magnetic flux #Mathematics #Perpendicular #Phase (matter) #Physics #Plane (geometry) #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #Quantum electrodynamics #Quantum mechanics #Spectral Theory in Mathematical Physics #Statistical physics #quant-ph
paper · pdf · doi:10.1016/s0375-9601(00)00608-3
published in Physics Letters A 276(1-4), 16-18 (Elsevier BV) · 5 pages, LaTeX 2e
arxiv created 2000/05/10 · openalex publication_date 2000/10/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider a two-dimensional particle of charge e interacting with a homogeneous magnetic field perpendicular to the plane and a potential well which is transported along a closed loop in the plane. We show that a bound state corresponding to a simple isolated eigenvalue acquires at that Berry's phase equal to 2π\rm sgn e times the number of flux quanta through the oriented area encircled by the loop. We also argue that this is a purely quantum effect since the corresponding Hannay angle is zero.