2013/02/25 by V. Kapoor, Varun Kapoor, Michael Ruggenthaler +2
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Density functional theory #Floquet theory #Hamiltonian (control theory) #Kohn–Sham equations #Laser-Matter Interactions and Applications #Mathematical optimization #Mathematical physics #Mathematics #Nonlinear system #Physics #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #physics.atom-ph #quant-ph
paper · pdf · doi:10.1103/physreva.87.042521
published as Phys. Rev. A 87, 042521 (2013) · 8 pages, 3 figures, PDFLatex, RevTeX
arxiv created 2013/02/25 · openalex publication_date 2013/04/30 · openalex created_date 2016/06/24 · arxiv updated 2017/11/21 · openalex updated_date 2026/08/05
The Floquet theorem allows one to reformulate periodic time-dependent problems such as the interaction of a many-body system with a laser field in terms of time-independent, field-dressed states, also known as Floquet states. If this was possible for density-functional theory as well, one could reduce in such cases time-dependent density-functional theory to a time-independent Floquet density-functional theory. We analyze under which conditions the Floquet theorem is applicable in a density-functional framework. By employing numerical ab initio solutions of the interacting time-dependent Schr"odinger equation with time-periodic external potentials we show that the exact effective potential in the corresponding Kohn-Sham equation is not unconditionally periodic. Whenever several Floquet states in the interacting system are involved in a physical process the corresponding Hartree-exchange-correlation potential is not periodic with the external frequency only. Using an analytically solvable example we demonstrate that, in general, the periodicity of the time-dependent Kohn-Sham Hamiltonian cannot be restored by choosing a different initial state. Only if the external periodic potential is sufficiently weak such that the initial state of the interacting system evolves adiabatically to a single, field-dressed state, the resulting Kohn-Sham system admits the application of the Floquet theorem.