1997/08/27 by R. Narevich, R Narevich, D. Spehner +3
Physics and Astronomy · #Asymptotic expansion #Domain (mathematical analysis) #Energy (signal processing) #Extension (predicate logic) #Heat kernel #Kernel (algebra) #Magnetic field #Quantum and electron transport phenomena #Quantum chaos and dynamical systems #Quantum many-body systems #Scattering #cond-mat.mes-hall
paper · pdf · doi:10.1088/0305-4470/31/18/016
13 pages, Revtex
arxiv created 1997/08/27 · openalex publication_date 1998/05/08 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
We present analytical methods to calculate the magnetic response of non-interacting electrons constrained to a domain with boundaries and submitted to a uniform magnetic field. Two different methods of calculation are considered - one involving the large energy asymptotic expansion of the resolvent (Stewartson-Waechter) applies to separable systems, the other based on the small time asymptotic behaviour of the heat kernel (Balian-Bloch). Both methods are in agreement with each other but differ from results previously obtained by Robnik. Finally, the Balian-Bloch multiple scattering expansion is studied and the extension of our results to other geometries is discussed.