没有运动方程的瞬子演算：从黎曼曲面的单值性出发的半经典
Instanton calculus without equations of motion: semiclassics from monodromies of a Riemann surface
摘要：
半经典量子力学中的瞬子计算依赖于沿轨道的积分，该积分求解经典运动方程。然而，在具有更高维度或复杂相空间的系统中，这些是很难实现的。一个主要的例子是自旋相干态，例如用于描述单分子磁体（SMM）。我们使用这个例子来开发瞬子微积分，它不依赖于经典运动方程的显式解。能量守恒将复相空间限制为复一维的黎曼曲面，允许根据柯西积分定理变形积分路径。因此，半经典作用量可以在不知道实际经典路径的情况下进行计算。此外，我们表明，在许多情况下，这样的行动可能只是来自monodromy相应的黎曼曲面和剩余值在其奇点的性质。作为一个例子，我们考虑淬火隧道过程中的SMM通过施加磁场。
英文摘要：
Instanton calculations in semiclassical quantum mechanics rely on integration along trajectories which solve classical equations of motion. However in systems with higher dimensionality or complexified phase space these are rarely attainable. A prime example are spin-coherent states which are used e.g. to describe single molecule magnets (SMM). We use this example to develop instanton calculus which does not rely on explicit solutions of the classical equations of motion. Energy conservation restricts the complex phase space to a Riemann surface of complex dimension one, allowing to deform integration paths according to Cauchy's integral theorem. As a result, the semiclassical actions can be evaluated without knowing actual classical paths. Furthermore we show that in many cases such actions may be solely derived from monodromy properties of the corresponding Riemann surface and residue values at its singular points. As an example, we consider quenching of tunneling processes in SMM by an applied magnetic field.
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