On the instability of an oscillator in a field - Efimov, Garij V.; Waldenfels, Wilhelm von (Annals of physics, 1994)
We discuss the origin of dissipation in a one-dimension model describing the interaction of a microsystem (an oscillator) with a bath (a quantized field). The Hamiltonian is a gauge-type coupling of the oscillator with the field and it is bounded below. Classical and quantum pictures are considered. Our formulation of the problem: what stable states are described by the total Hamiltonian if the excited states of the oscillator are unstable? How can these unstable states arise in a conservative system? The vacua of the free and the interacting system are found in dipole approximation. The theory determines a formfactor which optimizes the contributions of the total Hamiltonian in dipole approximation. These two vacua generate equivalent representations of canonical commutation relations. As a result of the oscillator-field interaction the stable states of this system consist of the vacuum (oscillator ground state) and quanta of the quantized field (bath). It means that 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.
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