We investigate the Calderón problem for the fractional Schrödinger equation with drift, proving that the unknown drift and potential in a bounded domain can be determined simultaneously and uniquely by an infinite number of exterior measurements. In particular, in contrast to its local analogue, this nonlocal problem does not enjoy a gauge invariance. The uniqueness result is complemented by an associated logarithmic stability estimate under suitable apriori assumptions. Also uniqueness under finitely many generic measurements is discussed. Here the genericity is obtained through singularity theory which might also be interesting in the context of hybrid inverse problems. Combined with the results from Ghosh et al. (Uniqueness and reconstruction for the fractional Calderón problem with a single easurement, 2018. arXiv:1801.04449), this yields a finite measurements constructive reconstruction algorithm for the fractional Calderón problem with drift. The inverse problem is formulated as a partial data type nonlocal problem and it is considered in any dimension \(n\ge 1\).

我们研究了带有漂移的分数阶Schrödinger方程的Calderón问题，证明了无限范围的外部测量可以同时且唯一地确定有界域中的未知漂移和电势。尤其是，相对于本地的模拟，这个外地问题并不能享受规范不变性。在适当的先验假设下，唯一性结果得到相关对数稳定性估计的补充。还讨论了在有限的许多常规测量下的唯一性。这里的通用性是通过奇点理论获得的在混合逆问题的背景下这可能也很有趣。结合Ghosh等人的结果。（只需一次确定就可以解决分数阶卡尔德隆问题的唯一性和重建，2018年。arXiv：1801.04449），这产生了带有漂移的分数阶卡尔德隆问题的有限度量构造性重建算法。逆问题被表述为部分数据类型的非局部问题，可以在任何维度\（n \ ge 1 \）中考虑。