Thermal Transport in a Noncommutative Hydrodynamics

Understand

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.