2007/04/28 by Roi Baer · 5 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum chaos and dynamical systems #Quantum many-body systems #cond-mat.dis-nn #cond-mat.other
paper · pdf · doi:10.1063/1.2822124
arxiv created 2007/04/28 · openalex publication_date 2008/01/24 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The mapping of time-dependent densities on potentials in systems of identical quantum mechanical particles is examined. This mapping is of significance ever since Runge and Gross [Phys. Rev. Lett. 52, 997 (1984)] established its uniqueness, forming the theoretical basis for time-dependent density functional theory. Beyond uniqueness there are two important issues: existence, often called v-representability, and stability. We show that v-representability for localized densities in turn-on situations is not assured and we give a simple example of nonexistence. As for stability, we discuss an inversion procedure and by computing its Lyapunov exponents we demonstrate that the mapping is unstable with respect to fluctuations in the initial state. We argue that such instabilities will plague any inversion procedure.