基于信息论的非线性薛定谔方程的性质
Properties of some nonlinear Schrodinger equations motivated through information theory
摘要：
我们更新我们的理解，通过信息论的非线性薛定谔方程的动机。特别是，我们表明，$q-$变形的基本非线性方程导致系统的能量的扰动增加，从而有利于最简单的$q=1$的情况下。此外，能量最小化标准被证明是等价的，在领先的顺序，不确定性最大化的论点。内插参数的特殊值$η=1/4$，其中前导阶能量位移消失，意味着在非线性超对称量子力学中现有的超对称性的保持。物理上，$η$可能编码相对论效应。
英文摘要：
We update our understanding of nonlinear Schrodinger equations motivated through information theory. In particular we show that a $q-$deformation of the basic nonlinear equation leads to a perturbative increase in the energy of a system, thus favouring the simplest $q=1$ case. Furthermore the energy minimisation criterion is shown to be equivalent, at leading order, to an uncertainty maximisation argument. The special value $η=1/4$ for the interpolation parameter, where leading order energy shifts vanish, implies the preservation of existing supersymmetry in nonlinearised supersymmetric quantum mechanics. Physically, $η$ might be encoding relativistic effects.
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