Suppression of radiation damping in electromagnetic waveguide: Signature of quantum decoherence in the field bath

Recent development of spectral analysis of the Liouville-von Neumann equation has revealed the fact that irreversibility is a rigorous dynamical property of Poincaré non-integrable systems with an infinite degrees of freedom interacting among each other through resonance coupling. In the present work we discuss this role of resonance in some examples of matter-field coupling systems for both classical and quantum mechanics: the one is a classical motion of a charged particle in electromagnetic waveguide, and the other is the decoherence problem of quantum matter-field interacting systems.; In the first part of this dissertation, we study an accelerated motion of a charged classical dipole molecule with frequency ω₁ inside the rectangular waveguide. If the particle is in free space, it is well known that its accelerated motion will eventually stop by radiating the field through the resonance interaction. This result is the so-called radiation damping. For the case in the waveguide, there are two possible situations, due to the existence of the cut-off frequency ω_c of the waveguide. Under the cut-off frequency electromagnetic wave cannot propagate inside the waveguide. The stability of the dipole depends on the relation between ω₁ and ω_c. For ω₁ < _c, the dipole cannot resonate with the field. This corresponds to the Poincaré integrable system. For this case the dipole keeps its accelerated motion without emitting the radiating field. Therefore the radiation damping of the dipole molecules is suppressed inside the waveguide under the absence of resonance interaction. The motion of this steady state somewhat resembles a quantum ground state. We show that this steady state is dressed by electromagnetic field. The overlap of the dressing field leads to a force analogous to van der Waals force in quantum mechanics. The critical frequency determined by ω₁ = ω_c, gives a critical size of the waveguide. For heavy molecules, such as HCl, this is of order 10−5m. We show that the size of the dressing field is the same order of the size of the waveguide. Hence we have a macroscopic size of the dressing in the waveguide.; For ω₁ > ω_c, the dipole can resonate with the field, and the system becomes non-integrable in the sense of Poincaré. (Abstract shortened by UMI.)...