Ballistic Particle Transport and Drude Weight in Gases

Area of Science:

• Quantum physics
• Statistical mechanics

Background:

• Particle transport in nonrelativistic gases is ballistic and characterized by the Drude weight.
• The Drude weight is calculable via linear response theory and relates to gas density (Δ=2πD).
• This applies to all dimensions and equilibrium ensembles, including generalized Gibbs ensembles for integrable quantum systems.

Purpose of the Study:

• To rigorously calculate the Drude weight for the integrable Lieb-Liniger Bose gas.
• To investigate its behavior within generalized Gibbs ensembles.
• To compare results with generalized hydrodynamics predictions.

Main Methods:

• Utilizing a generalized Yang-Yang thermodynamic formalism.
• Calculating generalized susceptibility related to conserved particle current fluctuations.
• Applying linear response theory.

Main Results:

• The Drude weight for the Lieb-Liniger Bose gas was rigorously calculated in generalized Gibbs ensembles.
• The derived expression aligns with predictions from generalized hydrodynamics.
• Demonstrated that conductivity in these ensembles is not solely determined by current-current autocorrelation functions.

Conclusions:

• The generalized Yang-Yang formalism provides a rigorous method for calculating Drude weights in integrable quantum systems.
• Confirms the applicability of generalized hydrodynamics in these scenarios.
• Highlights nuances in conductivity calculations for generalized Gibbs ensembles.