Mathematical and Theoretical Physics Seminar

Abstract: Systems Biology is a young and rapidly evolving research field, which combines experimental techniques and mathematical modeling in order to achieve a mechanistic understanding of processes underlying the regulation and evolution of living systems. Physics has a long tradition of characterizing and understanding emergent collective behaviors in systems of interacting units and searching for universal laws. Therefore, it is natural that many concepts used in Systems Biology have their roots in Physics. With an emphasis on Theoretical Physics, I will here review the ‘Physics core’ of Systems Biology, show how some success stories in Systems Biology can be traced back to concepts developed in Physics, and discuss how Systems Biology can further benefit from its Theoretical Physics foundation.

Abstract: We review the theory of the BCS to BEC to Insulator crossover in a two band model of doped bulk semiconductors with attractive interactions between the charge carriers and derive the superconducting order parameter, the quasiparticle density of states and the chemical potential as a function of the semiconductor gap $\Delta_0$ and the doping level $\varepsilon$. We verify previous results for the quantum phase diagram finding BCS-Superconductor to Bose-Einstein-Condensation (BEC) and BEC to Insulator transitions as function of doping level and the size of the band gap in 2 and 3 dimensions. Next, we apply this theory to study the properties of inhomogenous semiconductors with spatially varying charge density, in particular superconducting p-n junctions. We derive the spatial variation of the superconducting order parameter along the p-n junction. As the potential difference across the junction leads to energy band bending, we find a spatial crossover between a BCS and BEC condensate, as the density of charge carriers changes across the p-n junction. Thus, we find that there can be BEC layers in the well controlled setting of doped semiconductors, where the doping level can be varied to change and control the thickness of BEC and insulator layers, making Bose Einstein Condensates thereby possibly accessible to experimental transport and optical studies in solid state materials. A. Niroula, G. Rai, S. Haas, S. Kettemann, Spatial BCS-BEC Crossover in Superconducting pn-Junctions, submitted to Phys. Rev. B, arXiv:1912.09699 (2019).

Abstract: With new optical clocks and laser interferometers in space new instruments are at work to measure the gravitational field of the Earth with highest precision. The measurement procedures as well as the highest precision make it necessary to employ General Relativity. Accordingly, in the talk a fully general relativistic approach to geodesy is presented. Starting from a stationary situation the fully relativistic geoid is defined. Since relativistic gravity has more degrees of freedom than Newtonian gravity, a second geoid has been found which is related to the rotational degrees of freedom of gravity. The methods to practically measure these geoids are described and the deviation from Newtonian gravity is discussed. In the outlook remaining tasks are outlined.