Quantum transport in the Ising chain: global vs local approach

We study energy and spin transport in a one-dimensional Ising chain which is connected to two separate heat baths on both sides. By applying the Born-Markov approximation, within the global approach, we derive the Markovian master equation of the system, and also the explicit form of the Lindblad operators and the steady state. Thereafter, we investigate the behavior of energy and spin dynamics of the system in the global regime. Finally, we solve the problem with the local approach, and we show that the results are not the same for both approaches.