The project is focused on correlations and dynamics of one dimensional quantum many-body systems on the hydrodynamic scale.

The significance of low dimensional quantum systems stems from various aspects. On the one hand low dimensionality enhances quantum fluctuations, so these systems are often strongly correlated. On the other hand, distinguished members of this class of models are the so-called integrable systems which allow for the non-perturbative description of strongly interacting quantum systems. Apart from their theoretical significance, these systems can be studied experimentally both in condensed matter systems (spin chains, carbon nanotubes etc.) and with trapped ultra-cold atoms.

Even though integrability provides us with nontrivial information and allow us to use special techniques, it leaves many unanswered questions. For example, correlation functions are notoriously hard to calculate even in equilibrium. The out of equilibrium dynamics, especially in inhomogeneous systems, is even more difficult to access.

However, the recent years have seen a revolution thanks to the breakthrough given by the development of Generalized Hydrodynamics (GHD), a theory which captures the dynamics of integrable systems on the hydrodynamic level [1]. GHD was originally proposed to describe inhomogeneous systems, but the original works [2] spurred an immense activity and the theory has been evolving ever since. Among other achievements, it delivered long-awaited results about quantum transport in 1D, and now it allows us to study dynamical correlation functions, fluctuations, and even integrability breaking effects. Importantly, its predictions have been experimentally verified in cold atomic systems [3].

The goal of the project is to apply the recently developed framework of GHD to systems like the Calogero-Sutherland and Haldane-Shastry models in which the formalism becomes simpler. This can lead to new insights about the hydrodynamics of these long-range interacting systems.

The work requires both analytic and numerical calculations. The project gives an opportunity to learn about spin chains and low dimensional quantum field theories and to master various techniques, including the young theory of GHD.

[1] B. Doyon, Lecture notes on Generalised Hydrodynamics, SciPost Phys. Lect. Notes 18, (2020).

[2] O. A. Castro-Alvaredo, B. Doyon, and T. Yoshimura, Emergent Hydrodynamics in Integrable Quantum Systems Out of Equilibrium, Phys. Rev. X 6, 041065 (2016);
     B. Bertini, M. Collura, J. De Nardis, and M. Fagotti, Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents, Phys. Rev. Lett. 117, 207201 (2016). 

[3] M. Schemmer, I. Bouchoule, B. Doyon, and J. Dubail, Generalized Hydrodynamics on an Atom Chip, Phys. Rev. Lett. 122, 090601 (2019);
   N. Malvania, Y. Zhang, Y. Le, J. Dubail, M. Rigol, and D. S. Weiss, Generalized hydrodynamics in strongly interacting 1D Bose gases, Science 373, 1129 (2021).