Quantum thermalization and hydrodynamics have emerged as intriguing fields of research in quantum physics, shedding light on the equilibration and collective behavior of quantum systems. Both analytical and numerical methods to study the behavior of these systems in the many-particle and long-time limit are notoriously rare. Hydrodynamical descriptions, on the other hand, offers a powerful tool for integrable systems and low-energy effective theories. Our research aims to explore and establish the connection between the two, focusing on the emergence of hydrodynamic behavior in isolated quantum systems.

The Kardar-Parisi-Zhang (KPZ) universality class is a fundamental concept in the field of statistical physics, describing the behavior of a wide range of physical systems. It encompasses various phenomena, including surface growth, interface dynamics, and fluctuating interfaces. The KPZ universality class is characterized by the presence of roughening transitions and scaling properties that are independent of the specific details of the system. In an ongoing collaboration our group has found evidence for KPZ behavior in the thermalization of isolated quantum systems. Currently we are working on proofs explaining these observations.

Another active area of research within this field is many-body localization (MBL). This phenomenon arises when spatial inhomogeneity, most well-known disorder, stabilizes the dynamics of a system, effectively leading to localization of particles, even on long time scales. This behavior is in stark contrast to thermalization which generically features delocalization. Current research directions in MBL involve studying its universal properties and the nature of quantum phase transitions in localized systems. Experimental investigations aim to realize and probe MBL in various platforms such as ultracold atoms and NV centers. Theoretical efforts involve developing new models, refining numerical techniques, and exploring the connections between MBL and other areas such as quantum entanglement and quantum chaos.

Given the notion that quantum thermalization can be a long process, quantum simulation can be used to go beyond the capabilities of classical machines. Advances in the precise control of quantum many-body systems in the ultracold atom community open vast possibilities to study quantum dynamics and thermalization. We are working on developing methods to prepare nontrivial thermal, aka Gibbs, states at tunable temperatures using these platforms. In combined efforts with experiments, our goals include studying thermalization in these controlled many-body systems to better understand the underlying mechanisms.