04-80 Takuya Mine

The Aharonov-Bohm solenoids in a constant magnetic field (778K, Postscript) Mar 12, 04

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We study the spectral properties of two-dimensional magnetic Schr\"odinger operator $H_N= (\frac{1}{i}\nabla + \a_N)^2$. The magnetic field is given by $\rot \a_N = B+\sum_{j=1}^N 2\pi\alpha_j \delta(z-z_j)$, where $B>0$ is a constant, $1\leq N \leq \infty$, $0<\alpha_j<1$ $(j=1,\ldots,N)$ and the points $\{z_j\}_{j=1}^N$ are uniformly separated. We give an upper bound for the number of eigenvalues of $H_N$ between two Landau levels or below the lowest Landau level, when $N$ is finite. We prove the spectral localization of $H_N$ near the spectrum of the single solenoid operator, when $\{z_j\}_{j=1}^N$ are far from each other, all the values $\{\alpha_j\}_{j=1}^N$ are the same and the boundary conditions at all $z_j$ are the same. We give a characterization of self-adjoint extensions of the minimal operator.

Files: 04-80.src( 04-80.keywords , Aharonov_Bohm_Solenoids.ps )