LFU:online

Department of Theoretical Physics Department of Theoretical Physics

Dr. Michael Ruggenthaler Dr. Michael Ruggenthaler

705910

Density Functional Theories

VO 2

4

weekly

not applicable

English

The goal of this lecture is to give an introduction into ground-state density-functional theory (DFT) and its time-dependent generalization, so-called time-dependent density-functional theory (TDDFT). The focus lies on the theoretical foundations of these approaches.

DFT is one of the most popular approaches to (numerically) determine the ground-state properties of many-body systems. It finds its application in a variety of fields, e.g., condensed matter theory, quantum chemistry or nuclear physics. Although less well developed, also TDDFT has become a standard tool, e.g., to calculate optical excitation spectra of large molecules. This lecture will focus almost exclusively on the foundations of those two approaches to the many-body problem of quantum mechanics. Outline: 1. Motivation and Introduction (The quantum many-body problem and an example) 2. Many-Body Quantum Mechanics (Brief review of one-particle quantum mechanics in connection with L^p spaces, self-adjoint operators and Sobolev spaces; (anti)symmetrization of the many-body wave function and second quantization; the one-particle density) 3. Ground-State Density-Functional Theory (Properties of the densities and the energy-functional; Hohenberg-Kohn theorems; functional derivative and the Kohn-Sham construction; the local density approximation) 4. Time-Dependent Density-Functional Theory (Quantum fluid dynamics; Runge-Gross and van Leeuwen theorem; linear response theory) 5. If time permits and dependening on the choice of the students (Approximations like the GGA or orbital functionals; relativistic (TD)DFT; connection to Keldysh Green's function techniques...)

E. Engel and R.M. Dreizler, "Density Functional Theory - An Advanced Course", (Springer, Heildeberg, 2011) C.A. Ullrich, "Time-Dependent Density-Functional Theory - Concepts and Application" (Oxford University Press, Oxford, 2012) P. Blanchard and E. Brüning, "Mathematical Methods in Physics - Distributions, Hilbert Space Operators and Variational Methods" (Birkhäuser, Boston, 2003) Links to nice overviews of the theories: http://theochem.chem.rug.nl/publications/Abstracts.html#425 http://zernike.eldoc.ub.rug.nl/root/2001/IntJModPhysBvLeeuwen/?pLanguage=en&pFullItemRecord=ON