A relaxation theory of strongly coupled quantum dissipative systems

Mio Murao, Fumiaki Shibata

Brett Min, Matthew Gerry, Dvira Segal

We focus on a dissipative three-level system as a case study to analytically demonstrate that strong system-bath coupling separates the relaxation dynamics of this dissipative quantum system into two distinct regimes: a short-time dynamics that, as expected, accelerates with increasing coupling to the environment, and a slow dynamics that, counterintuitively, becomes prolonged at sufficiently strong coupling. Using the reaction-coordinate polaron-transform mapping, we uncover the general mechanism behind this effect and derive accurate expressions for both relaxation timescales. Numerical simulations confirm our analytical predictions. From a practical perspective, our results suggest that strong coupling to a dissipative bath can autonomously generate and sustain long-lived quantum coherences, offering a promising strategy for bath-engineered quantum state preparation.

Ilya Prigogine

Alex Stewart-Bozzo, Jakub Garwoła, Brett Min +1 more

We investigate the dissipative dynamics of multilevel quantum systems strongly coupled either to a lossy cavity mode or directly to a bosonic environment. By deriving spectral localization bounds, we establish conditions under which strong system-bath coupling gives rise to a hierarchy of population relaxation timescales. Our approach builds on the reaction-coordinate polaron-transform framework. By mapping the original strong-coupling problem onto an effective weakly dissipative model, we analyze the spectrum of the resulting Liouvillian superoperator through localization bounds. For the generalized V model, we find that strong system-bath coupling gives rise to a bright-dark structure in the effective system-bath coupling operator: a single collective mode remains strongly coupled to the environment, while the remaining modes become progressively dark. Consequently, the dynamics separate into fast and slow sectors and, at finite coupling strengths, develop a hierarchy of population relaxation timescales. Numerical simulations based on both secular and non-secular quantum master equations corroborate the emergence of timescale separation and the pronounced slowing down of dissipative dynamics at strong coupling. Our results reveal a general mechanism underlying anomalously slow relaxation in strongly coupled open quantum systems and provide a route for engineering long-lived states through system-environment interactions.

Lucas Sá, Pedro Ribeiro, Tomaž Prosen

We propose the Sachdev-Ye-Kitaev Lindbladian as a paradigmatic solvable model of dissipative many-body quantum chaos.It describes N strongly coupled Majorana fermions with random all-to-all interactions, with unitary evolution given by a quartic Hamiltonian and the coupling to the environment described by M quadratic jump operators, rendering the full Lindbladian quartic in the Majorana operators.Analytical progress is possible by developing a dynamical mean-field theory for the Liouvillian time evolution on the Keldysh contour.By disorder-averaging the interactions, we derive an (exact) effective action for two collective fields (Green's function and self-energy).In the large-N, large-M limit, we obtain the saddle-point equations satisfied by the collective fields, which determine the typical timescales of the dissipative evolution, particularly the spectral gap that rules the relaxation of the system to its steady state.We solve the saddle-point equations numerically and find that, for strong or intermediate dissipation, the system relaxes exponentially, with a spectral gap that can be computed analytically, while for weak dissipation, there are oscillatory corrections to the exponential relaxation.In this letter, we illustrate the feasibility of analytical calculations in strongly correlated dissipative quantum matter.