论文标题
谐波陷阱中莱维过程的绝热捷径的快捷方式
Shortcuts To Adiabaticity for Lévy processes in harmonic traps
论文作者
论文摘要
Lévy随机过程具有根据Lévy稳定分布分布的噪声，在科学中无处不在。为了关注被困在外部谐波电位中的粒子的情况，我们解决了找到“达到绝热捷径”的问题：在以给定的初始固定状态制备系统后，我们为驱动外部电位寻找时间依赖的协议，以便在给定的有限时间中达到给定的最终状态。这些技术通常用于具有加性高斯噪声的随机过程，通常是基于反向工程方法。我们通过在傅立叶空间中找到相关特征函数的精确方程来概括在过度阻尼和阻尼失败的方案中，对更广泛的Lévy随机过程的方法概括了方法。
Lévy stochastic processes, with noise distributed according to a Lévy stable distribution, are ubiquitous in science. Focusing on the case of a particle trapped in an external harmonic potential, we address the problem of finding "shortcuts to adiabaticity": after the system is prepared in a given initial stationary state, we search for time-dependent protocols for the driving external potential, such that a given final state is reached in a given, finite time. These techniques, usually used for stochastic processes with additive Gaussian noise, are typically based on a inverse-engineering approach. We generalise the approach to the wider class of Lévy stochastic processes, both in the overdamped and in the underdamped regime, by finding exact equations for the relevant characteristic functions in Fourier space.
