论文标题
通过具有次级排斥潜力的Schrödinger算子的强大传播估计值，波算子的不存在
Nonexistence of wave operators via strong propagation estimates for Schrödinger operators with sub-quadratic repulsive potentials
论文作者
论文摘要
亚偏端排斥电势加速量子颗粒，并可以放松外部电位$ v $的$ x $中的衰减率，以保证量子波算子的存在。如果亚二次电势为$ - | x |^α$，$ 0 <α<2 $并且外部电位满足$ | v（x）| \ leq c（1+ | x |） ^{ - （1-α/2） - \ varepsilon} $，带有$ \ varepsilon> 0 $，bony et。 Al [3]确定了波算子的存在和完整性，然后Itakura [12，13，14]随后使用固定散射理论获得了其结果，从而获得了更广义的外部电位。根据他们的结果，我们自然会期望以下内容。如果外部电势$ V $的衰减功率小于$ { - （1-α/2）} $，则V包含在短期类中。如果衰减功率大于或等于$ { - （1-α/2）} $，则$ v $包含在远程类中。在这项研究中，我们首先证明了可以应用于散射理论的时间传播器的新传播估计。其次，我们证明，如果功率大于或等于$ - （1-α/2）$，并且使用新的传播估计值是正确的，则波动算子不存在。
Sub-quadratic repulsive potentials accelerate quantum particles and can relax the decay rate in the $x$ of the external potentials $V$ that guarantee the existence of the quantum wave operators. In the case where the sub-quadratic potential is $- |x|^α $ with $0< α< 2$ and the external potential satisfies $|V(x) | \leq C (1+|x|) ^{-(1- α/2) - \varepsilon} $ with $\varepsilon>0$, Bony et. al [3] determined the existence and completeness of the wave operators, and Itakura [12, 13, 14] then obtained their results using stationary scattering theory for more generalized external potentials. Based on their results, we naturally expect the following. If the decay power of the external potential $V$ is less than ${ -(1- α/2) } $, V is included in the short-range class. If the decay power is greater than or equal to ${ -(1- α/2) } $, $V$ is included in the long-range class. In this study, we first prove the new propagation estimates for the time propagator that can be applied to scattering theory. Second, we prove that the wave operators do not exist if the power is greater than or equal to $-(1- α/2)$ and that the threshold expectation of ${ -(1- α/2) } $ is true using the new propagation estimates.
