论文标题
多个井的空气 - schr {Ö} dinger操作员和周期性通风的状态的集成密度{Ö} dinger操作员
Multiple wells Airy-Schr{ö}dinger operator and integrated density of states of the periodic Airy-Schr{ö}dinger operator
论文作者
论文摘要
我们计算一个明确的公式，以实现真实线上的周期性通风schr {Ö} dinger操作员的整合密度。为此，我们精确地研究了对周期性通风schr {Ö} dinger操作员限制到有限的时期的范围。我们证明，该限制的所有特征值都在周期性的shr {Ö} dinger操作员的光谱带中，并且它们都没有在光谱差距中。我们准确地计算了每个光谱频段中特征值的数量，该数量等于周期性操作员受到限制的周期数，还有一个。请注意，我们的结果取决于半经典参数，但在半经典限制中没有说明。它们对大于显式常数的半经典元值有效。
We compute an explicit formula for the integrated density of states of the periodic Airy-Schr{ö}dinger operator on the real line. For this purpose, we study precisely the spectrum of the restriction of the periodic Airy-Schr{ö}dinger operator to a finite number of periods. We prove that all the eigenvalues of this restriction are in the spectral bands of the periodic Airy-Schr{ö}dinger operator and none of them are in its spectral gaps. We count exactly the number of eigenvalues in each of the spectral bands, this number being equal to the number of periods to which the periodic operator is restricted, plus one. Note that our results depends on a semiclassical parameter but are not stated in the semiclassical limit. They are valid for values of the semiclassical larger than explicit constants.
