Thermal Transport in a Noncommutative Hydrodynamics

TL;DR

This work develops a finite-temperature hydrodynamic framework for electrons confined to the lowest Landau level by linking noncommutative geometry to a Hamiltonian formulation with Poisson brackets. It shows that the most general hydrodynamics arises when the Righi-Leduc (thermal Hall) coefficient $c_{RL}$ is allowed to depend on thermodynamic variables, and it derives Středa-type relations and energy-transport structures that include an energy magnetization $M_E$. In the high-temperature limit, the authors obtain closed-form expressions for $c_{RL}$ in terms of dilogarithms, demonstrating its smooth interpolation between low-filling and full-filled regimes and its compatibility with particle-hole symmetry. The results provide a principled basis for thermal Hall transport in LLL systems and lay groundwork for incorporating dissipation and Coulomb effects in future extensions.

Abstract

We find the hydrodynamic equations of a system of particles constrained to be in the lowest Landau level. We interpret the hydrodynamic theory as a Hamiltonian system with the Poisson brackets between the hydrodynamic variables determined from the noncommutativity of space. We argue that the most general hydrodynamic theory can be obtained from this Hamiltonian system by allowing the Righi-Leduc coefficient to be an arbitrary function of thermodynamic variables. We compute the Righi-Leduc coefficients at high temperatures and show that it satisfies the requirements of particle-hole symmetry, which we outline.