Title :
Short-wavelength asymptotics for the low Landau zones of the two-dimensional magnetic Schrödinger operator
Author :
Pankrashkin, Konstantin V. ; Poteryakhin, Mikhail A.
Author_Institution :
Inst. of Math., Humboldt-Univ., Berlin, Germany
Abstract :
We study an asymptotic behavior of the bottom part for the spectrum of the two-dimensional magnetic Schrödinger operator with uniform magnetic and periodic electric fields. Using averaging methods we reduce the corresponding classical problem to a one-dimensional Hamiltonian system on the torus and obtain almost invariant manifolds of the original Hamiltonian. Asymptotics of the spectrum is constructed now by means of the canonical operator with a complex germ
Keywords :
Landau levels; Schrodinger equation; electric fields; magnetic fields; mathematical operators; spectral analysis; 2D magnetic Schro¨dinger operator; averaging methods; canonical operator; complex germ; invariant manifolds; low Landau zones; one-dimensional Hamiltonian system; periodic electric fields; short-wavelength asymptotics; spectral series; spectrum; torus; two-dimensional magnetic Schro¨dinger operator; uniform magnetic fields; Diffraction; Energy states; Environmental factors; History; Mathematics;
Conference_Titel :
Day on Diffraction 2001. Proceedings. International Seminar
Conference_Location :
St.Petersburg
Print_ISBN :
5-7997-0366-9
DOI :
10.1109/DD.2001.988477
