Spectral truncation of out-of-time-ordered correlators in dissipative systems.

Area of Science:

• Quantum physics
• Quantum information science

Background:

• Out-of-time-ordered correlators (OTOCs) are key diagnostics for quantum chaos and information scrambling.
• Their behavior in dissipative (open quantum) systems is less understood than in closed systems.

Purpose of the Study:

• Investigate the spectral decomposition of OTOCs in open quantum systems.
• Develop efficient modeling techniques for OTOC dynamics in dissipative environments.

Main Methods:

• Utilized the dissipative modified kicked rotator as a model system.
• Analyzed the eigenvalue spectrum of the quantum Liouvillian.
• Identified a spectral truncation criterion for modeling OTOCs.

Main Results:

• Discovered two distinct temporal regimes for OTOC dynamics: long-time decay and an intermediate-time regime.
• The spectral gap governs long-time decay, while subdominant eigenvalues are crucial in the intermediate regime.
• Established a direct link between eigenvalue structure and information scrambling.

Conclusions:

• The spectral truncation criterion enables efficient modeling of OTOC decay in open quantum systems.
• Provides a quantitative framework for understanding quantum chaos and information scrambling in dissipative systems.
• Suggests new experimental directions for open quantum platforms.