Thermal Transport in a Noncommutative Hydrodynamics

TL;DR

This paper develops a hydrodynamic theory for particles in the lowest Landau level, incorporating noncommutative geometry, and explores the behavior of Righi-Leduc coefficients at high temperatures.

Contribution

It introduces a Hamiltonian framework for noncommutative hydrodynamics and generalizes the Righi-Leduc coefficient as a thermodynamic function.

Findings

Righi-Leduc coefficient computed at high temperatures.

The theory respects particle-hole symmetry.

Hydrodynamics derived from noncommutative geometry.

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.