论文标题
具有复杂衰减电势的随机Schrödinger操作员
Random Schrödinger operators with complex decaying potentials
论文作者
论文摘要
我们证明，Anderson类型的连续体随机schrödinger操作员的特征值$-Δ+v_Ω$具有复杂的衰减潜力，可以在所有$ q \ q \ leq d+ 1 $的潜力的$ l^q $规范方面受到限制（概率很高）。这表明，在随机环境中，指数$ q $与弗兰克（Bull。Lond。Math。Soc。，2011年）相比，可以将指数$ Q $从本质上翻了一番。这种改进是基于波尔加因的思想（离散连续的dyn。Syst。，2002），与晶格Schrödinger运营商几乎确定的散射有关。
We prove that the eigenvalues of a continuum random Schrödinger operator $-Δ+ V_ω$ of Anderson type, with complex decaying potential, can be bounded (with high probability) in terms of an $L^q$ norm of the potential for all $q\leq d+1$. This shows that in the random setting, the exponent $q$ can be essentially doubled compared to the deterministic bounds of Frank (Bull. Lond. Math. Soc., 2011). This improvement is based on ideas of Bourgain (Discrete Contin. Dyn. Syst., 2002) related to almost sure scattering for lattice Schrödinger operators.
