论文标题
量子和Koopman动力学中的谐波统一转换
Free to Harmonic Unitary Transformations in Quantum and Koopman Dynamics
论文作者
论文摘要
长期以来，已经知道存在一个坐标转换，该坐标转换精确地映射了量子谐波振荡器。在这里，我们通过将其重新定义为单一操作，然后进行时间坐标转换来扩展此结果。我们证明，在Koopman von-Neumann（KVN）动力学的背景下，可以对经典系统进行等效的转换。我们进一步将此映射扩展到量子和经典情况下的耗散演变，并表明该映射赋予了两种动力学的耗散参数的相同时间依赖性缩放。派生的经典程序提供了许多机会，将相关量子程序（例如哈密顿的放大）进口到经典制度。
It has long been known that there exists a coordinate transformation which exactly maps the quantum free particle to the quantum harmonic oscillator. Here we extend this result by reformulating it as a unitary operation followed by a time coordinate transformation. We demonstrate that an equivalent transformation can be performed for classical systems in the context of Koopman von-Neumann (KvN) dynamics. We further extend this mapping to dissipative evolutions in both the quantum and classical cases, and show that this mapping imparts an identical time-dependent scaling on the dissipation parameters for both types of dynamics. The derived classical procedure presents a number of opportunities to import squeezing dependent quantum procedures (such as Hamiltonian amplification) into the classical regime.
