Relaxation and decay of collective modes in open quantum systems

In a quantum many-body system, such as atoms, molecules, and atomic nuclei, interparticle interactions generate a complex quantum level scheme that can be analyzed progressively: from the simplest picture of independent quasiparticles moving in a self-consistent mean field to more complete descriptions that include residual interactions and the opening of decay channels above some excitation thresholds. Residual interactions lead to two seemingly contrasting phenomena: the emergence of collective modes (such as rotational and vibrational excitations) associated with specific symmetries, and internal thermalization, which gives rise to features of quantum chaos and causes these collective modes to damp. The picture becomes more intricate once decay channels become energetically accessible, allowing the system to decay irreversibly by means such as particle emission and thus transition to an open quantum regime. In this work, we investigate the competition between internal many-body dynamics and explicit, irreversible decay. These processes can occur on comparable timescales, leading to an initial stage of rapid dynamics followed by equilibration. We show that the decay of the faster components drives the system into an exponentially decaying regime, characterized by a noisy decay current. For this study, we adopt a general, albeit simplified, model of a collective mode embedded in a chaotic background and coupled to open decay channels. The interplay of timescales revealed in this framework appears to reflect universal features of open quantum systems.