Complex Systems

• Disordered Quantum Spin Systems: We investigate disordered systems with local quantum degrees of freedom, such as spins or tunnel systems with long-range interactions. Such systems exist in metals with magnetic impurities, doped semiconductors, and glasses and can be used as qubits for quantum computers. In order to control and read out qubits, we need a detailed understanding of their properties. The combination of disorder and long-range interaction makes this a challenging fundamental problem (funded by DFG in cooperation with S. Haas, USC LA, R. Bhatt, Princeton Univ. in the United States). 
• Metal-insulator Transitions: We are conducting research into the theory of metal-insulator transitions in disordered quantum systems. This requires the nonperturbative modeling of localisation, multifractality of electron wave functions, and dynamic local magnetic moments. We are undertaking this research in collaboration with K. Slevin at Osaka University in Japan, T. Ohstuki Sophia University in Japan, and K.-S. Kim at Postech in South Korea). 
• Inhomogeneous Superconductors: We are researching the theory of inhomogeneous superconductors and the crossover between BCS-Superconductivity and Bose-Einstein condensation. We are investigating novel quantum states of matter at the BCS-BEC crossover in a two-dimensional crystalline material at the atomic scale. We are exploring new physics at the junction of the BCS-BEC crossover regime such as enhanced critical current and novel Andreev bound states. We are undertaking this research in collaboration with S. Haas at the University of Southern California Los Angeles in the United States; G. Raj at Hamburg University in Germany; and X. Chen and S.-H. Ji at Tsinghua University in China.
• Dynamics and Stability of Transmission and Distribution Grids: We are modeling and analyzing the propagation of disturbances in transmission and distribution grids. Building on new insights, we aim to develop appropriate control strategies to prepare for the transition towards high shares of renewable energy. We employ response theory combined with spectral analysis of the nonlinear coupled differential equations, together with numerical differential equation solvers and deep learning methods. This research is funded by BMBF-CoNDyNet and CoNdyNet2 in cooperation with H. Meyer-Ortmanns, G. Brunekreeft and several institutes including the Potsdam-Institut für Klimafolgenforschung and Forschungszentrum Jülich in Germany.

• We discovered novel excited states, so called Rainbow states, with supercritical entanglement in disordered quantum spin chains with power-law long-range antiferromagnetic couplings, see Fig. 1 and Ref. [1]. 
• We discovered spatial BCS-BEC crossover in superconducting pn-junctions, see Fig. 2 and Ref. [2].
• We developed a real-time response theory with delayed control for the 3rd model of transmission grids, see Fig. 3 and Refs. [3,5].
• We modeled and conducted a disturbance analysis of transmission grids of African countries, including Nigeria, Ghana, and Rwanda [4].
• We co-organized the international conferences Localisation 2020 and Localisation 2022 in Sapporo, Japan and coedited its Proceedings in Annals of Physics in memory of P. W. Anderson, Princeton University.

In 2022 the Complex Systems Group consisted of one Postdoctoral fellow and two PhD students funded by the joint BMBF project CoNDyNet and one DFG individual grant.

• Y. Mohdeb, J. Vahedi, S. Kettemann, Excited-Eigenstate Entanglement Properties of XX Spin Chains with Random Long-Range Interactions, Phys. Rev. B 106, 104201 (2022). 
• A. Niroula, G. Rai, S. Haas, S. Kettemann, Spatial BCS-BEC Crossover in Superconducting pnJunctions, Phys. Rev. B 101, 094514 (2020). 
• P. C. Böttcher, A. Otto, S. Kettemann, C. Agert, Time delay effects in the control of synchronous electricity grids, CHAOS 30, 013122 (2020). 
• K. P. Nnoli, S. Kettemann, Spreading of Disturbances in Realistic Models of Transmission Grids: Dependence on Topology, Inertia and Heterogeneity, Scientific Reports 11, 23742 (2021). 
• D. Witthaut, F. Hellmann, J. Kurths, S. Kettemann, H. Meyer-Ortmanns, M. Timme, Collective Nonlinear Dynamics and Self- Organization in Decentralized PowerGrids, Reviews of Modern Physics, 394, 015005 (2022).