论文标题
在分数时间方案中，两级量子系统的统一进化
Unitary evolution for a two-level quantum system in fractional-time scenario
论文作者
论文摘要
从分数schrödinger方程（FTSE）获得的时间进化运算符被认为是非单身的，因为它不能及时保留矢量状态的规范。如在时间依赖性的非量子形式主义中所做的那样，对于一个无可观的非温和两级量子系统，我们证明可以在单一单位中绘制非单一的时间进化运算符。它是通过考虑具有时间依赖的度量运算符的动态希尔伯特空间，该空间是由遗传学时间依赖性的dyson地图构建的，该地图以单一的方式演变而成，并且可以正确地进行标准的量子力学解释。为了阐明我们的方法，我们考虑了三个示例的哈密顿运营商及其从FTSE解决方案以及相应的Dyson地图获得的相应统一动力学的例子。
The time-evolution operator obtained from the fractional-time Schrödinger equation (FTSE) is said to be non-unitary since it does not preserve the norm of the vector state in time. As done in the time-dependent non-Hermitian quantum formalism, for a traceless non-Hermitian two-level quantum system, we demonstrate that it is possible to map the non-unitary time-evolution operator in a unitary one. It is done by considering a dynamical Hilbert space with a time-dependent metric operator, constructed from a Hermitian time-dependent Dyson map, in respect to which the system evolves in a unitary way, and the standard quantum mechanics interpretation can be made properly. To elucidate our approach, we consider three examples of Hamiltonian operators and their corresponding unitary dynamics obtained from the solutions of FTSE, and the respective Dyson maps.
