ON THE INSTABILITY OF AN OSCILLATOR IN A FIELD

We discuss the origin of dissipation in a one-dimension model describi ng the interaction of a microsystem (an oscillator) with a bath (a qua ntized field). The Hamiltonian is a Puge-type coupling of the oscillat or with the field and it is bounded below. Classical and quantum Pictu res are considered. Our formulation of the problem: what stable states are described by the total Hamiltonian if the excited states of the o scillator are unstable? How can these unstable states arise in a conse rvative system? The vacua of the free and the interacting system are f ound in dipole approximation. The theory determines a formfactor which optimizes the contributions of the total Hamiltonian in dipole approx imation. These two vacua generate equivalent representations of canoni cal commutation relations. As a result of the oscillator-field interac tion the stable states of this system consist of the vacuum (oscillato r ground state) and quanta of the quantized field (bath). It means tha t the oscillator as a stable state can exist only in the ground state. Any excited oscillator states can be seen as resonances in the field- field scattering. (C) 1994 Academic Press. Inc