论文标题

磁性schrödinger操作员的痕量公式及其应用

Trace formulas for magnetic Schrödinger operators on periodic graphs and their applications

论文作者

Korotyaev, Evgeny, Saburova, Natalia

论文摘要

我们考虑具有周期性离散图上具有周期性磁性和电势的Schrödinger操作员。此类操作员的光谱由有限数量的频段组成。我们确定磁性schrödinger算子的痕量公式。纤维操作员的痕迹表示为Quasimomentum的有限傅立叶系列。傅立叶系列的系数是根据一些特定循环集的商图中的磁通量,电势和循环给出的。使用痕量公式,我们从图,磁通量和电势的几何参数方面,获得了磁性schrödinger操作员总带宽的新较低估计值。我们表明这些估计值很清晰。

We consider Schrödinger operators with periodic magnetic and electric potentials on periodic discrete graphs. The spectrum of such operators consists of a finite number of bands. We determine trace formulas for the magnetic Schrödinger operators. The traces of the fiber operators are expressed as finite Fourier series of the quasimomentum. The coefficients of the Fourier series are given in terms of the magnetic fluxes, electric potentials and cycles in the quotient graph from some specific cycle sets. Using the trace formulas we obtain new lower estimates of the total bandwidth for the magnetic Schrödinger operator in terms of geometric parameters of the graph, magnetic fluxes and electric potentials. We show that these estimates are sharp.

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