非绝热电磁场引起的希尔伯特空间几何变化
Hilbert space geometry change by a nonadiabatic electromagnetic field
- Technical University of Sofia（索菲亚理工大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究发现非绝热电磁场使量子系统希尔伯特空间几何改变，量子态由正交变为非正交，并给出时间相关Fubini-Study度量，类比广义相对论时空度量。
AI中文摘要：
发现了一个与非绝热电磁场相互作用的量子系统的希尔伯特空间几何变化。为确定其物理起源，基于量子态矩阵元，在三种主要物理情形下研究了量子系统状态从正交性到非正交性的演化：零外场中的量子系统（封闭量子系统）、缓慢变化（绝热）场中的量子系统，以及快速变化（非绝热）场中的量子系统。在前两种情形下，量子态是正交的；而在非绝热场中，量子态变为非正交，并连续地跟随场的参数变化。在非绝热情形下，可基于量子态矩阵元确定希尔伯特空间的时间相关Fubini-Study度量。量子力学中这种希尔伯特空间的动力学度量类似于广义相对论中时空的动力学度量。
英文摘要：
A change in the geometry of the Hilbert space of a quantum system interacting with a nonadiabatic electromagnetic field is found. To identify its physical origin, the evolution of orthogonality to non-orthogonality of the states of the quantum system has been investigated based on the matrix elements of the quantum states in three main physical cases: a quantum system in zero external field (closed quantum system), a quantum system in slowly changing (adiabatic) field, and a quantum system in rapidly changing (nonadiabatic) field. The quantum states are orthogonal in the first two cases and change to non-orthogonal in a nonadiabatic field, following continuously the parameters of the field. A time-dependent Fubini-Study metric of the Hilbert space can be determined based on the matrix elements of the quantum states in the nonadiabatic case. Such a dynamical metric of the Hilbert space in quantum mechanics resembles the dynamical metric of spacetime in general relativity.
