Functional differentiability in time-dependent quantum mechanics

Abstract

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.

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• Differentiable but exact formulation of density-functional theory
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Cited by in corpus (4)

• Existence, Uniqueness, and Construction of the Density-Potential Mapping in Time-Dependent Density-Functional Theory
• Invertibility of the retarded response functions for initial mixed states: application to one-body reduced density matrix functional theory
• Invertibility of retarded response functions for Laplace transformable potentials: application to one-body reduced density matrix functional theory
• Regularity for evolution equations with non-autonomous perturbations in Banach spaces