零次渐近齐次二维电磁势的经典和量子动力学
Classical and quantum dynamics for 2D-electromagnetic potentials asymptotically homogeneous of degree zero
摘要：
考虑在电磁势作用下沿平面运动的带电粒子，其径向极限不为零。我们分析的经典和量子动力学的情况下，大的时间（限制）洛伦兹力（定义为纯径向的速度）的角度部分有一个有限数量的零在固定的能量。任何这样的零点都定义了一个通道，我们将量子波算符与“稳定”的通道联系起来。研究了它们在磁通量为零和非零情况下的完备性。在后一种情况下，人们可能需要纳入一个螺旋状态的通道。这些状态类似于最近在\cite {CHS}中研究的符号确定的情况。
英文摘要：
We consider a charged particle moving in the plane subject to electromagnetic potentials with non-vanishing radial limits. We analyse the classical and the quantum dynamics for large time in the case the angular part of the (limiting) Lorentz force (defined for velocities that are purely radial) has a finite number of zeros at fixed energy. Any such zero defines a channel, and to the "stable" ones we associate quantum wave operators. Their completeness is studied in the case of zero as well as nonzero magnetic flux. In the latter case one needs possibly to incorporate a channel of spiraling states. These states are similar to those studied recently in the sign-definite case in \cite {CHS}.
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