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The quantum dissipative dynamics of a tunneling process through doublebarrier structures is investigated on the basis of a rigorous treatment for thefirst time. We employ a Caldeira-Leggett Hamiltonian with an effectivepotential calculated self-consistently, accounting for the electrondistribution. With this Hamiltonian, we use the reduced hierarchy equations ofmotion in the Wigner space representation to study the effects of non-Markovianthermal fluctuations and dissipation at finite temperature in a rigorousmanner. Hysteresis, double plateau-like behavior, and self-excited currentoscillation are observed in a negative differential resistance (NDR) region ofthe current-voltage curve. We find that while most of the current oscillationsdecay in time in the NDR region, there is a steady oscillation characterized bya tornado-like rotation in the Wigner space in the upper plateau of the NDRregion.

An approach to quantum transport based on reduced hierarchy equations of motion: Application to a resonant tunneling diode