Generalized Hydro Dynamics (GHD) is a novel, very powerful tool to describe 1d systems. After a very brief introduction, I will first present a way to extend GHD to the dimensional cross over regime  and highlight the experimental tests of standard and extended GHD. In the second part of my talk, I will highlight how GHD can give us a much-improved understanding of the excitations and their decay/dephasing in a 1d Bose gas, and thereby highlighting the relationship between many-body interactions and dimensionality. In our experiments we prepare a single mode of excitations and watch it decay. We find that the decay of the excitations is perfectly described with GHD and 1D behavior can extend deep into the three-dimensional (3D) crossover. Our observations demonstrate that the fundamental excitations are not phonons but are rapidities assuming fermionic statistics, despite the gas being purely bosonic . The rapid damping of phonons can 1d can be understood as the dephasing the rapidities.
Supported by DFG-FWF: SFB ISOQUANT.
 F. Moller, et al., Phys.Rev.Lett. 126, 090602 (2021)
 F. Cataldini et al., Phys. Rev. X 12, 041032 (2022)
Jörg Schmiedmayer is a Professor of Experimental Physics at the Faculty of Physics at the TU-Wien, Vienna, Austria. He was a founding member of the Vienna Centre for Quantum Science and Technology. Schmiedmayer is one of the pioneers of matter wave interferometry and quantum simulation science. His invention of micro traps for neutral atoms and the AtomChip triggered a new field of research, micro-manipulation of atoms, ions and molecules. His research on non equilibrium evolution and relaxation started a new direction in many body quantum science and continues to inspire new research directions world wide. His detailed analysis of correlations in many body quantum systems started a new field in quantum information science: quantum simulation of quantum field theories and emerging quantum simulators which have to be contrasted with simple building the hamiltonian directly in the lab as in Hubbard models. He is a recipient of several prestigious grants and awards, including the Wittgenstein Prize. He is full member of the Austrian Academy of Sciences.