"The interaction between electrons renders a direct solution of the fundamental equation of quantum mechanics, the Schrödinger equation, a formidable task, which can only be achieved for systems comprised of just a few degrees of freedom. In order to numerically describe systems which are comparable in size to actual experiments approximations are unavoidable. Within thermal DFT these approximations manifest themselves in the form of effective potentials shaping the charge and energy distribution of the electrons. Within this project we tackled the construction of approximations for these effective potentials along two research lines: 1) Approximations based on the uniform electron gas, a paradigm for interacting electrons. 2) Approximations based on impurity models, which have recently attracted a lot of attention, because they showed some promise in describing strongly interacting electrons. Based on the electron gas we constructed a so-called adiabatic local-density approximation. However, we realized that the required input, the free energy of the interacting electron gas, is, at least for the moment, not available in the required accuracy. Using impurity models we were able to devise novel approximation which take retardation effects into account. Furthermore, we understood how the effective potentials from impurity models can be generalized to study transport devices at experimentally relevant scales. In order to perform such large scale simulations, we derived (semi-)analytic methods to simulate the dynamics of electrons exposed to a temperature gradient and a potential bias.
In the course of this project we presented our findings at various national and international conferences and workshops. The ER presented contributed talks at both the DPG spring meeting and APS March meeting in 2017 and 2018 respectively:
• 2017 „Charge and energy transport at the Nanoscale: A DFT perspective “
• 2018 „Transient charge and energy flow in the wide-band limit “
Furthermore, results were presented at specialized workshops in Europa and USA in form of invited and contributed talks.
• 2016 Workshop: Time-Dependent Density-Functional Theory: Prospects and Applications in Benasque, Spain; „Thermal density-functional theory: Towards the ab-initio description of thermoelectric transport at the nano scale “(invited talk)
• 2017 Workshop: Excited States: Electronic Structure and Dynamics in Telluride, U.S.A.; „Charge and Energy Transport at the Nanoscale: A Density-Functional Theory Perspective “(invited talk)
• 2018 ETSF Workshop 2018, Milano, Italy; „Time-dependent charge and energy transport in nanoscale devices “(contributed talk)
We also addressed the general public during the ""Open Door Day 2017"" with a popular science talk titled “The Beautiful Invisible” at the hosting institution in an effort to underline the importance and promote the fascination for fundamental research.
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