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We discuss the problem of heat conduction in quantum spin chain models. Toinvestigate this problem it is necessary to consider the finite open systemconnected to heat baths. We describe two different procedures to couple thesystem with the reservoirs: a model of stochastic heat baths and the quantumtrajectories solution of the quantum master equation. The stochastic heat bathprocedure operates on the pure wave function of the isolated system, so that itis locally and periodically collapsed to a quantum state consistent with aboundary nonequilibrium state. In contrast, the quantum trajectories procedureevaluates ensemble averages in terms of the reduced density matrix operator ofthe system. We apply these procedures to different models of quantum spinchains and numerically show their applicability to study the heat flow.

Heat Transport in Quantum Spin Chains: Stochastic Baths vs Quantum Trajectories