Alexander Jahn

The number of grant applications is rising sharply. Our capacity for their evaluation isn’t. ERC President Maria Leptin explains why stricter resubmission limits are being introduced for 2027 calls and what this mean for applicants. link.europa.eu/xF7kjc

Very happy to have this paper with @jenseisert and his PhD student Shozab Qasim out on the @arxiv! It achieves something that, until recently, I thought to be impossible: To use random tensor networks to study holographic *dynamics*.

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Random #tensornetworks provide a powerful framework for probing and understanding complex quantum systems, especially in regimes where conventional tools fail. Here, we rigorously investigate dynamical properties of #holographic toy models. scirate.com/arxiv/2508.165… In detail, recent years have enjoyed substantial progress in capturing properties of complex quantum systems by means of #randomtensornetworks (RTNs), which form ensembles of quantum states that depend only on the tensor network geometry and bond dimensions. Of particular interest are RTNs on hyperbolic geometries, with local tensors typically chosen from the unitary Haar measure, that model critical boundary states of holographic #bulkboundary dualities. In this work, we elevate static pictures of ensemble averages to a dynamical one, to show that RTN states exhibit equilibration of time-averaged operator expectation values under a highly generic class of Hamiltonians with non-degenerate spectra. We prove that RTN states generally equilibrate at large bond dimension and also in the scaling limit for three classes of geometries: Those of #matrixproductstates, regular #hyperbolictilings, and single "black hole" tensors. Furthermore, we prove a hierarchy of #equilibration between finite-dimensional instances of these classes for bulk and boundary states with small entanglement. This suggests an equivalent hierarchy between corresponding many-body phases, and reproduces a holographic degree-of-freedom counting for the effective dimension of each system. These results demonstrate that RTN techniques can probe aspects of late-time dynamics of quantum many-body phases and suggest a new approach to describing aspects of holographic dualities using techniques from statistical mechanics. Warm thanks to Shozab Qasim and @PhysicistAlex for the fruitful collaboration. And thanks to our funders, specifically at the @dfg_public (#CRC183 and #FOR2724), and the @ERC_Research.