In this project, the structure of and constraints on quasihydrodynamics were investigated. One of the key objectives was to demonstrate that it was possible to write a consistent (quasi-)hydrodynamic theory around stationary states with relaxation. To achieve this, the researcher began by generalising the Drude model which is a phenomenological description for charge flow in a material to a hydrodynamic derivative expansion. The condition relating the velocity of the charge carriers to the phenomenological momentum loss term, a key assumption of the Drude model, became the defining relation for the stationary flow of a fluid. Subsequently, the suite of non-dissipative transport coefficients and DC conductivities were derived allowing us to achieve the initial goal.
Having completed one research objective, the researcher turned to the second – determining the range of validity of quasihydrodynamics. One avenue of research suggested in the original proposal was to consider anomalous hydrodynamics, a particularly constrained quasihydrodynamic theory. Several results for the thermo-electric conductivities of this theory in the presence of a weak, external magnetic field were known in the literature and in mutual contradiction. This naturally represented a challenge to the validity of the quasihydrodynamic framework. However, the researcher managed to resolve this issue by considering the same models with strong magnetic fields and then taking the small field limit, thus allowing us to arrive at a single consistent answer.
In, tackling this inconsistency, the grantee had at one point shown that standard hydrodynamics constraints – namely, Onsager reciprocity – were not satisfied by some of the literature results. This naturally led to questioning how this symmetry (and the related partner constraint of positivity of entropy production) appear in a quasihydrodynamic theory. In a series of works these constraints were examined and seen to restrict the space of possible relaxation terms. Moreover, in achieving this objective, standard kinetic theory was extended to include generic relaxation terms.
The results of this action have been disseminated through six scientific publications in peer-reviewed journals and presentations at five conferences/workshops. One of the papers is an invited review of the grantee's previous work in the field of relaxed hydrodynamics. All the papers are available on the arXiv so that the wider public has access to the results.
