Beyond hydrodynamics

Marie Skłodowska-Curie Actions Grant agreement ID: 101030915

An illustrative example of how the hydrodynamic regime occurs. Localised perturbations (imagine moving one of the blue dots) are quickly dissipated among the bath of blue particles. Large perturbations, such as collecting particles to one side of the green tube, take much longer to spread out as they only diffuse through the individual particles colliding with each other. This latter perturbation is a "hydrodynamic perturbation".

Hydrodynamics is the framework by which we can understand the evolution of interacting systems at late times and large distances. It is particularly appropriate for predicting the behaviour of strongly interacting systems. In such cases, localised or short time perturbations rapidly thermalise due to their interactions with the rest of the system. Consequently, only conserved charges such as: the energy, the momentum or particle number are relevant for describing the system's development at moderate to late time scales. As these charges cannot be destroyed the only way that the system can return to global thermodynamic equilibrium is for perturbations of these "hydrodynamic charges" to spread out.

As hydrodynamics concerns the conserved charges it is perhaps not surprising that the governing equations of motion are precisely the conservation equations for those charges. In relativistic theories for example, conservation of energy and momentum correspond to conservation of the stress-energy-momentum tensor. To these equations one must also supply the "constitutive" relations. These are expressions for the charge currents, such as the energy current, in terms of the hydrodynamic charges (energy, momentum and particle number). The constitutive relations are derivative expansions with each derivative being treated as progressively smaller. Intuitively one can understand that constant values for the hydrodynamic charges in space, corresponding to global thermodynamic equilibrium, trivialise these relations as all the derivatives vanish.

Quasihydrodynamics is an evolution of hydrodynamics to allow for some of the hydrodynamic charges to decay very slowly. This is accomplished by the addition of relaxation terms to the charge conservation equations. This framework is underdeveloped compared to its much more widely applied cousin. The purpose of this project was to begin an initial foray into formalising the field of relaxed hydrodynamics.

Publications:

For further discussion - see the relevant subpage.

Conferences:

“Relaxed hydrodynamics (a very brief overview)” (28/09/23) - Invited talk at Hydrodynamics at all Scales workshop at Nordita, Stockholm, Sweden.
“Relaxed hydrodynamics” (07/09/23) - Invited talk at CMD 30 FisMat 2023, Milano, Genova.
"A hydrodynamic description for transport in the strange metal phase of cuprates" (09/03/23) - Presentation at the APS March Meeting, Las Vegas.
“A hydrodynamic description for transport in the strange metal phase of cuprates” (25/07/22) - Poster presentation at the International Conference on Strongly Correlated Electron Systems in Amsterdam, The Netherlands.
“Relaxed hydrodynamics with an external electric field - or the Drude model” (28/06/22) - Spotlight talk at the Recent Developments in Strongly Correlated Quantum Matter conference in Stockholm, Sweden.

Further publications produced after the grant period:

Further relevant reading by the author:

This project has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 101030915.