Expansion potentials for exact far-from-equilibrium spreading of particles and energy

TL;DR

This paper introduces 'expansion potentials' as state functions controlling far-from-equilibrium energy and particle spreading in quantum systems, linking nonequilibrium dynamics to equilibrium response functions.

Contribution

It establishes a universal thermodynamic framework connecting far-from-equilibrium spreading rates to integrals of equilibrium Drude weights, verified through DMRG simulations.

Findings

Energy and particle spreading rates are governed by expansion potentials.

Expansion potentials are expressed as integrals of equilibrium Drude weights.

Non-equilibrium Maxwell relations for Drude weights are derived.

Abstract

The rates at which energy and particle densities move to equalize arbitrarily large temperature and chemical potential differences in an isolated quantum system have an emergent thermodynamical description whenever energy or particle current commutes with the Hamiltonian. Concrete examples include the energy current in the 1D spinless fermion model with nearest-neighbor interactions (XXZ spin chain), energy current in Lorentz-invariant theories or particle current in interacting Bose gases in arbitrary dimension. Even far from equilibrium, these rates are controlled by state functions, which we call ``expansion potentials'', expressed as integrals of equilibrium Drude weights. This relation between nonequilibrium quantities and linear response implies non-equilibrium Maxwell relations for the Drude weights. We verify our results via DMRG calculations for the XXZ chain.