论文标题
一般动力不变的及其统一关系的表述，以依赖于时间依赖的耦合量子振荡器
Formulation of general dynamical invariants and their unitary relations for time-dependent coupled quantum oscillators
论文作者
论文摘要
使用liouville-von neumann方程得出了与时间相关耦合振荡器的确切不变算子。代表了两个不耦合的简单谐波振荡器的不变与不变的不变之间的统一关系。如果我们认为简单谐波振荡器的量子解决方案是众所周知的，那么这种单一关系对于阐明原始系统的量子特性非常有用，例如纠缠，概率密度，规范变量的波动和腐烂。我们可以通过成反转换属于简单谐波振荡器的量子数量的数学表示来确定此类量子特征。作为一个很好的例子，通过与简单谐波振荡器相关的众所周知的本征函数的反变形，可以找到原始系统中不变型操作员的征函数。
An exact invariant operator of time-dependent coupled oscillators is derived using the Liouville-von Neumann equation. The unitary relation between this invariant and the invariant of two uncoupled simple harmonic oscillators is represented. If we consider the fact that quantum solutions of the simple harmonic oscillator is well-known, this unitary relation is very useful in clarifying quantum characteristics of the original systems, such as entanglement, probability densities, fluctuations of the canonical variables, and decoherence. We can identify such quantum characteristics by inversely transforming the mathematical representations of quantum quantities belonging to the simple harmonic oscillators. As a case in point, the eigenfunctions of the invariant operator in the original systems are found through inverse transformation of the well-known eigenfunctions associated with the simple harmonic oscillators.
