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Within the hierarchical quantum master equation (HQME) framework, an approachis presented, which allows a numerically exact description of nonequilibriumcharge transport in nanosystems with strong electronic-vibrational coupling.The method is applied to a generic model of vibrationally coupled transportconsidering a broad spectrum of parameters ranging from the nonadiabatic to theadiabatic regime and including both resonant and off-resonant transport. Weshow that nonequilibrium effects are important in all these regimes. Inparticular in the off-resonant transport regime, the inelastic co-tunnelingsignal is analyzed for a vibrational mode in full nonequilibrium, revealing acomplex interplay of different transport processes and deviations from thecommonly used $G_0/2$-thumb-rule. In addition, the HQME-approach is used tobenchmark approximate master equation and nonequilibrium Green's functionmethods.

Hierarchical Quantum Master Equation Approach to Electronic-Vibrational Coupling in Nonequilibrium Transport through Nanosystems