  The quantum dissipative dynamics of a tunneling process through double
barrier structures is investigated on the basis of non-perturbative and
non-Markovian treatment. 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 non-Markovian and
non-perturbative thermal effects at finite temperature in a rigorous manner. We
study current variation in time and the current-voltage (I-V) relation of the
resonant tunneling diode for several widths of the contact region, which
consists of doped GaAs. Hysteresis and both single and double plateau-like
behavior are observed in the negative differential resistance (NDR) region.
While all of the current oscillations decay in time in the NDR region in the
case of a strong system-bath coupling, there exist self-excited high-frequency
current oscillations in some parts of the plateau in the NDR region in the case
of weak coupling. We find that the effective potential in the oscillating case
possesses a basin-like form on the emitter side (emitter basin) and that the
current oscillation results from tunneling between the emitter basin and the
quantum well in the barriers. We find two distinct types of current
oscillations, with large and small oscillation amplitudes, respectively. These
two types of oscillation appear differently in the Wigner space, with one
exhibiting tornado-like motion and the other exhibiting a two piston
engine-like motion.
