1999/09/30 by Pavel Exner, Masao Hirokawa, Osamu Ogurisu · 3 citations
Chemistry · Mathematics · Physics and Astronomy · #Anomalous magnetic dipole moment #Bound state #Chemistry #Condensed matter physics #Electron #Flux (metallurgy) #Magnetic field #Magnetic flux #Magnetic moment #Mathematical analysis #Mathematical physics #Mathematics #Operator (biology) #Pauli exclusion principle #Physics #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #Quantum mechanics #Spectral Theory in Mathematical Physics #Spectrum (functional analysis) #Upper and lower bounds #cond-mat #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1023/a:1007679721268
published in Letters in Mathematical Physics 50(2), 103-114 (Springer Science+Business Media) · 12 pages, LaTeX2e; the final version, to appear in Lett. Math. Phys
openalex publication_date 1999/10/01 · arxiv created 2000/02/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider a two-dimensional electron with an anomalous magnetic moment, g>2, interacting with a nonzero magnetic field B perpendicular to the plane which gives rise to a flux F. Recent results about the discrete spectrum of the Pauli operator are extended to fields with the O(r-2-δ) decay at infinity: we show that if |F| exceeds an integer N, there is at least N+1 bound states. Furthermore, we prove that weakly coupled bound states exist under mild regularity assumptions also in the zero flux case.