Compact and complete description of non-Markovian dynamics

Area of Science:

• Quantum dynamics
• Theoretical chemistry
• Condensed matter physics

Background:

• Generalized master equations model diverse quantum processes, but their time-nonlocal memory description is complex.
• A need exists for more compact and intuitive descriptions of these dynamics.

Purpose of the Study:

• To demonstrate the utility of the time-convolutionless formalism as a compact description of quantum dynamics.
• To analyze its applicability and advantages over time-nonlocal methods.

Main Methods:

• Focus on dissipative dynamics of spin-boson and Frenkel exciton models.
• Constructing time-local generators from reference reduced dynamics.
• Analyzing parameter dependence and divergences.

Main Results:

• The time-convolutionless approach provides a compact, algorithmically simple, and physically interpretable description.
• It requires minimal information, comparable to time-nonlocal schemes.
• Methods to diagnose and circumvent apparent divergences were developed.

Conclusions:

• The time-convolutionless formalism offers significant advantages in describing quantum dynamics.
• Its discrete-time analog and protocol extend applicability to limited-resolution data.
• This work simplifies and reduces the cost of dynamical methods.