非线性平均场量子模型中可观测的本征态重叠
Observable eigenstate overlap in a nonlinear mean-field quantum model
摘要：
在非线性物理学中，孤子效应的定义是将非线性时变动力系统转化为等价的线性谱本征问题，其不变本征值明确定义了原系统的所有动力学性质。在非相对论各向同性双电子平均场量子点模型中，我们指出了这种效应的存在。它产生的预测，其两个最低能量的零角动量非线性本征态（即本征态，其中包括电子-电子相互作用：因此它们的非正交性）之间的辐射吸收的可观察到的调制。在GaAs的情况下，给出了这样一个可能的实验的特征值。此外，它提供了一个有趣的非线性定义的精细结构常数仅在这些本征态。
英文摘要：
The soliton effect is defined in nonlinear physics by the transformation of a nonlinear time-dependent dynamical system into an equivalent linear spectral eigenproblem whose invariant eigenvalues unambiguously define all the dynamical properties of the original system. We point out the existence of such an effect in a non-relativistic isotropic two-electron mean-field quantum-dot model. It yields the prediction of observable modulation of radiation absorption between its two lowest-energy zero-angular-momentum nonlinear eigenstates (i.e. eigenstates which include electron-electron interaction: hence their non-orthogonality). Characteristic values for such a possible experiment are given in the case of GaAs. Furthermore it provides an intriguing nonlinear definition of the fine-structure constant solely in terms of these eigenstates.
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