空间分数量子系统的静态超极化率
Static hyperpolarizability of space-fractional quantum systems
摘要：
研究了静态电场作用下空间分数阶量子力学系统的非线性响应。在粒子中心论的观点下，从分数阶薛定谔方程出发，导出了受广义Rieke Kuhn求和规则矩阵元约束的三能级模型的极化率和超极化率的表达式.这些表达式类似于半相对论系统，其中最大线性和非线性静态响应的减少归因于正则位置和动量换向器的函数依赖性。作为例子，我们研究了一个被剪裁的量子谐振子势和一个斜阱势。的线性和第一非线性响应的扰动场示出减少的空间分数进一步低于统一，这是由抑制的偶极跃迁矩。这些结果说明了影响系统光学响应强度的动力学动量算符的维数和阶数的重要性。
英文摘要：
The nonlinear response is investigated for a space-fractional quantum mechanical system subject to a static electric field. Expressions for the polarizability and hyperpolarizability are derived from the fractional Schrödinger equation in the particle-centric view for a three-level model constrained by the generalized Thomas-Rieke-Kuhn sum rule matrix elements. These expressions resemble those for a semi-relativistic system, where the reduction of the maximum linear and nonlinear static response is attributed to the functional dependence of the canonical position and momentum commutator. As examples, a clipped quantum harmonic oscillator potential and slant well potential are studied. The linear and first nonlinear response to the perturbing field are shown to decrease as the space fractionality is moved further below unity, which is caused by a suppression of the dipole transition moments. These results illustrate the importance of dimensionality and the order of the kinetic momentum operator which affect the strength of a system's optical response.
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