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Time inhomogeneous quantum dynamical maps
1Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5/7, 87-100, Toruń, Poland. darch@fizyka.umk.pl.
Scientific Reports
|December 9, 2022
Summary
This study introduces a new class of quantum evolution models using completely positive trace-preserving maps. These models describe time-inhomogeneous quantum systems and generalize master equations.
Area of Science:
- Quantum mechanics
- Quantum information theory
Background:
- Quantum evolution is typically described by time-homogeneous processes.
- Understanding time-inhomogeneous quantum dynamics is crucial for complex systems.
Purpose of the Study:
- To introduce and analyze a broad class of time-inhomogeneous quantum evolution.
- To develop a theoretical framework for non-Markovian quantum dynamics.
Main Methods:
- Construction of dynamical maps using infinite series of jump processes.
- Derivation of a time-inhomogeneous memory kernel master equation.
- Exploration of time-local (convolution-less) approaches.
Main Results:
- A two-parameter family of completely positive trace-preserving maps representing quantum evolution was established.
- The derived master equation generalizes standard convolution-based equations.
- A comparison between time-homogeneous and time-inhomogeneous quantum evolution was performed.
Conclusions:
- The proposed framework offers a versatile tool for studying complex quantum systems.
- The findings provide new insights into non-Markovian quantum dynamics.
- This work bridges the gap between time-local and non-local descriptions of quantum evolution.
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