  The quantum dissipative dynamics of a tunneling process through double
barrier structures is investigated on the basis of a rigorous treatment for the
first time. We employ a Caldeira-Leggett Hamiltonian with an effective
potential calculated self-consistently, accounting for the electron
distribution. With this Hamiltonian, we use the reduced hierarchy equations of
motion in the Wigner space representation to study the effects of non-Markovian
thermal fluctuations and dissipation at finite temperature in a rigorous
manner. Hysteresis, double plateau-like behavior, and self-excited current
oscillation are observed in a negative differential resistance (NDR) region of
the current-voltage curve. We find that while most of the current oscillations
decay in time in the NDR region, there is a steady oscillation characterized by
a tornado-like rotation in the Wigner space in the upper plateau of the NDR
region.
