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Heat transport in open quantum systems is particularly susceptible to themodeling of system-reservoir interactions. It thus requires to consistentlytreat the coupling between a quantum system and its environment. Whileperturbative approaches are successfully used in fields like quantum optics andquantum information, they reveal deficiencies, typically in the context ofthermodynamics, when it is essential to respect additional criteria such asfluctuation-dissipation theorems. We use a non-perturbative approach forquantum dissipative dynamics based on a stochastic Liouville-von Neumannequation to provide a very general and extremely efficient formalism for heatcurrents and its correlations in open harmonic chains. Specific results arederived not only for first but also for second order moments which requires toaccount for both real and imaginary parts of bath-bath correlation functions.Spatiotemporal patterns are compared with weak coupling calculations. Theregime of stronger system-reservoir couplings gives rise to an intimateinterplay between reservoir fluctuations and heat transfer far fromequilibrium.

Currents and fluctuations of quantum heat transport in harmonic chains