论文标题
量化Lévy航班
Quantizing Lévy flights
论文作者
论文摘要
量子布朗运动的Caldeira-Leggett模型使用通用速度依赖性耦合进行了推广。这导致了一组能够捕获布朗和莱维统计的模型的描述，具体取决于耦合的功能形式以及储层的光谱函数。发现一种特定的耦合力，该耦合力与\ textit {sisyphus}激光冷却中的冷原子的Lévy统计量建立了联系。在低速限制中，这也会引起布朗粒子的额外惯性，从而从亚伯拉罕·洛伦兹（Abraham-Lorentz）方程式从超级浴的第一原理中繁殖。通过欧几里得时代的路径综合量化，环境被整合在一起，留下了一组非本地有效作用。这些结果进一步充当了几个数值计算的起点，尤其是非荷花浴的破坏性特性。
The Caldeira-Leggett model of quantum Brownian motion is generalized using a generic velocity-dependent coupling. That leads to the description of a set of models able to capture Markovian and non-Markovian versions of Brownian and Lévy statistics, depending on the functional form of the coupling and on the spectral function of the reservoir. One specific coupling force is found that establishes a connection with Lévy statistics of cold atoms in \textit{Sisyphus} laser cooling. In the low-velocity limit, this also gives rise to additional inertia of the Brownian particle, reproducing the Abraham-Lorentz equation from first principles for a superohmic bath. Through path-integral quantization in Euclidean time, the environment is integrated out, leaving a set of non-local effective actions. These results further serve as starting points for several numerical calculations, particularly decoherence properties of non-ohmic baths.
