Location of Repository

Previous Up Next Article Citations From References: 2 From Reviews: 1



Propagators weakly associated to a family of Hamiltonians and the adiabatic theorem for the Landau Hamiltonian with a time-dependent Aharonov-Bohm flux. (English summary) J. Math. Phys. 46 (2005), no. 5, 053303, 26 pp. The adiabatic limit of the Laughlin-Halperin model for the quantum Hall effect (QHE) is at the heart of the mathematical physics literature on QHE. The authors discuss the existence of this adiabatic limit for the Hamiltonian corresponding to a constant magnetic field on R2 with an additional flux tube, without any electric potential. The magnetic flux of the tube is assumed to vary over the time interval τ. First of all, even the existence of the time evolution (propagator) is nontrivial: The Hamiltonian H(t) has a domain varying with t, and its time-derivative ˙ H(t) is not relatively bounded. The same is true in terms of the adiabatically rescaled time s, of course. The key idea for overcoming this difficulty goes back to [M. Born and V. Fock, Z. Phys. 51 (1928), 165–180; JFM 54.0994.03]: Replace H(s) by the adiabatic Hamiltonian Had(s): = H(s) + ı

Year: 2011
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.