Heat transport in an open transverse-field Ising chain

The heat conduction in an open transverse-field Ising chain is studied by using quantization in the Fock space of operators in the weak coupling regimes, i.e. the coupling is much smaller than the transverse field. The non-equilibrium steady state is obtained for large size systems coupled to Markovian baths at its ends. The ballistic transport is observed in the uniform chain and normal diffusion in the random-exchange chain. {In addition, the ballistic-diffusive transition is found at the intermediate disorder regime.} The thermal conductivity $\kappa$ is also calculated in the low and high temperature regimes. It is shown that $\kappa$ decays as $\kappa\sim T^{-2}$ at high temperatures.Comment: 6 pages, 7 figure

Markovian Master Equations: A Critical Study

We derive Markovian master equations of single and interacting harmonic systems in different scenarios, including strong internal coupling. By comparing the dynamics resulting from the corresponding Markovian master equations with exact numerical simulations of the evolution of the global system, we precisely delimit their validity regimes and assess the robustness of the assumptions usually made in the process of deriving the reduced dynamics. The proposed method is sufficiently general to suggest that the conclusions made here are widely applicable to a large class of settings involving interacting chains subject to a weak interaction with an environment.Comment: 40 pages, 14 figures, final versio