Geodesic
Asymptotic properties of the magnetic integrated density of states
Electronic journal of differential equations, Tome 1999 (1999)
This article could be regarded as a supplement to [11] where we considered the Schrodinger operator with constant magnetic field and decaying electric potential, and studied the asymptotic behaviour of the discrete spectrum as the coupling constant of the magnetic field tends to infinity. To describe this behaviour when the kernel of the magnetic field is not trivial, we introduced a measure ${\cal D}(\lambda )$ defined on $(-\infty,0)$ called the "magnetic integrated density of states". In this article, we study the asymptotic behaviour of this measure as $\lambda\uparrow 0$ and as $\lambda \downarrow \lambda_0, \lambda_0$ being the lower bound of the support of ${\cal D}$.
Classification : 35J10, 35P20, 81Q10
Keywords: magnetic Schrödinger operator, integrated density of states, spectral asymptotics 
@article{EJDE_1999__1999__a60,
     author = {Raikov,  G.D.},
     title = {Asymptotic properties of the magnetic integrated density of states},
     journal = {Electronic journal of differential equations},
     year = {1999},
     volume = {1999},
     zbl = {0921.35020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a60/}
}
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Raikov,  G.D. Asymptotic properties of the magnetic integrated density of states. Electronic journal of differential equations, Tome 1999 (1999). http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a60/