Dynamical Relaxation in Non-Relativistic QED: Resonances and Metastable States
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Abstract
We explore resonances and metastable states in non-relativistic quantum electrodynamics. When (N) bosonic particles interact with a free radiation field, their stable excited states dissolve into the continuous spectrum and become decaying metastable states. We use complex dilation, also known as spectral deformation, to analytically continue across the branch cut of the continuous spectrum and expose the corresponding resonance poles. Using a perturbative expansion followed by the Feshbach map, we derive the states’ second-order energy shifts and exponential decay rates and show that these rates agree with Fermi’s golden rule.