具有复衰减势的随机薛定谔算子
Random Schrödinger operators with complex decaying potentials
AI总结：
本文证明安德森型连续随机薛定谔算子（具复衰减势）的特征值可由势的L^q范数（q≤d+1）界定，随机情形下指数q较Frank的确定性界基本翻倍，改进基于Bourgain的几乎必然散射思想。
摘要：
我们证明，对于所有q≤d+1，安德森型连续随机薛定谔算子-Δ+V_ω（具有复衰减势）的特征值可（以高概率）用势的L^q范数界定。这表明在随机情形下，指数q与Frank（《伦敦数学会公报》，2011）的确定性界相比可基本翻倍。该改进基于Bourgain（《离散连续动力系统》，2002）关于格点薛定谔算子几乎必然散射的相关思想。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
