Penz Markus, Ruggenthaler Michael
Institut für Theoretische Physik, Universität Innsbruck, 6020 Innsbruck, Austria.
J Chem Phys. 2015 Mar 28;142(12):124113. doi: 10.1063/1.4916390.
In this work, we investigate the functional differentiability of the time-dependent many-body wave function and of derived quantities with respect to time-dependent potentials. For properly chosen Banach spaces of potentials and wave functions, Fréchet differentiability is proven. From this follows an estimate for the difference of two solutions to the time-dependent Schrödinger equation that evolve under the influence of different potentials. Such results can be applied directly to the one-particle density and to bounded operators, and present a rigorous formulation of non-equilibrium linear-response theory where the usual Lehmann representation of the linear-response kernel is not valid. Further, the Fréchet differentiability of the wave function provides a new route towards proving basic properties of time-dependent density-functional theory.
在这项工作中，我们研究了含时多体波函数以及关于含时势的导出量的泛函可微性。对于适当选取的势和波函数的巴拿赫空间，证明了弗雷歇可微性。由此得出了在不同势的影响下演化的含时薛定谔方程的两个解之差的一个估计。这样的结果可以直接应用于单粒子密度和有界算子，并且给出了非平衡线性响应理论的一个严格表述，其中线性响应核的通常莱曼表示是无效的。此外，波函数的弗雷歇可微性为证明含时密度泛函理论的基本性质提供了一条新途径。
