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Expansion potentials for exact far-from-equilibrium spreading of energy in the XXZ model

Presented by: 
Joel Moore University of California, Berkeley
Monday 11th January 2016 - 11:30 to 12:30
INI Seminar Room 1
Co-authors: Romain Vasseur (UC Berkeley), Christoph Karrasch (UC Berkeley; FU Berlin)

The rates at which energy and particle densities move to equalize arbitrarily large temperature and chemical potential differences in a closed 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 gas in arbitrary dimension. Even far from equilibrium, these rates are controlled by state functions (generalized pressures or "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 which explain some old XXZ model identities. We verify our results via DMRG calculations for the XXZ chain, which suggest some interesting additional fe atures beyond the analytical results.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons