Accelerated Decay due to Operator Spreading in Bulk-Dissipated Quantum Systems.

Area of Science:

• Quantum Physics
• Many-Body Systems
• Statistical Mechanics

Background:

• Markovian open many-body quantum systems exhibit complex relaxation dynamics.
• The Liouvillian spectral gap traditionally characterizes asymptotic decay rates but may not fully determine overall relaxation times.
• Limited understanding exists regarding relaxation processes preceding the long-time asymptotic regime.

Purpose of the Study:

• To investigate the collective relaxation dynamics of autocorrelation functions in the stationary state of quantum systems.
• To introduce and analyze a new metric, the instantaneous decay rate, for characterizing transient relaxation.
• To explore the relationship between instantaneous decay rate and asymptotic decay rates.

Main Methods:

• Analysis of collective relaxation dynamics in the stationary state.
• Introduction of the instantaneous decay rate as a key analytical quantity.
• Theoretical modeling of bulk-dissipated systems.

Main Results:

• The instantaneous decay rate characterizes transient relaxation and converges to the asymptotic decay rate in the long-time limit.
• Bulk-dissipated systems generically exhibit accelerated decay before the asymptotic regime.
• This accelerated decay is linked to the scrambling of quantum information and operator spreading.

Conclusions:

• The spectral gap alone is insufficient to describe the complete relaxation dynamics of open quantum systems.
• The instantaneous decay rate provides a more comprehensive understanding of transient relaxation phenomena.
• Quantum information scrambling plays a crucial role in the accelerated relaxation dynamics observed in these systems.