  We examine the Breit-Wigner resonances that ensue from field effects in
molecular single electron transistors (SETs). The adiabatic dynamics of a
quantum dot elastically attached to electrodes are treated in the
Born-Oppenheimer approach. The relation between thermal and shot noise induced
by the source-drain voltage $V_{bias}$ is found when the SET operates in a
regime tending to thermodynamic equilibrium far from resonance. The
equilibration of electron-phonon subsystems produces broadening and doublet
splitting of transparency resonances helping to explain a negative differential
resistance (NDR)of current versus voltage (I-V) curves. Mismatch between the
electron and phonon temperatures brings out the bouncing-ball mode in the
crossover regime close to the internal vibrations mode. The shuttle mechanism
occurs at a threshold $V_{bias}$ of the order of the Coulomb energy $U_c$. An
accumulation of charge is followed by the Coulomb blockade and broken symmetry
of a single or double well potential. The Landau bifurcation cures the
shuttling instability and the resonance levels of the quantum dot become split
because of molecular tunneling. We calculate the tunnel gaps of conductivity
and propose a tunneling optical trap (TOT) for quantum dot isolation permitting
coherent molecular tunneling by virtue of Josephson oscillations in a charged
Bose gas. We discuss experimental conditions when the above theory can be
tested.
