Ballistic particle transport and Drude weight in gases
Frank Göhmann, Andreas Klümper, Karol K. Kozlowski
TL;DR
The work shows that particle transport in Galilei-invariant gases is inherently ballistic and governed by a Drude weight Δ = 2πD, valid across dimensions and ensembles. It links Δ to a momentum-current susceptibility and validates this relation using linear-response theory and exact Yang-Yang/TBA methods for the Lieb-Liniger gas, with consistency to generalized-hydrodynamics results in thermal equilibrium. For generalized Gibbs ensembles, the Drude weight generalizes beyond simple current-current fluctuations, highlighting subtleties in interpreting conductivity and the limitations of DoSp-type matrix formulations. The findings have implications for interpreting cold-atom experiments and the role of integrability in ballistic transport, clarifying when GGEs reproduce or modify the standard Drude picture.
Abstract
Owing to the fact that the particle current operator in non-relativistic gases is proportional to the total momentum operator, the particle transport in such systems is always ballistic and fully characterized by a Drude weight $Δ$. The Drude weight can be calculated within linear response theory. It is given by the formula $Δ= 2 πD$, where $D$ is the density of the gas. This holds in any dimension and for every equilibrium ensemble, in particular for generalized Gibbs ensembles that describe possible equilibrium states of isolated integrable quantum systems. In the canonical ensemble case, the Drude weight can be equivalently obtained from a generalized susceptibility related to the fluctuations of the conserved particle current. Such susceptibility can be rigorously calculated for the integrable Lieb-Liniger Bose gas in any generalized Gibbs ensemble using a generalized Yang-Yang thermodynamic formalism. The resulting expression agrees with a prediction made within the context of generalized hydrodynamics. It also allows us to see explicitly that, within truly generalized Gibbs ensembles, the conductivity related with the particle current is not determined by the corresponding current-current auto-correlation function.