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Optimal form of time-local non-Lindblad master equations
Tobias Becker1, André Eckardt1
1Technische Universität Berlin, Institut für Theoretische Physik, Hardenbergstrasse 36, 10623 Berlin, Germany.
Physical Review. E
|April 18, 2025
Summary
Quantum master equations beyond weak coupling, like Redfield and Hu-Paz-Zhang, can be transformed into a pseudo-Lindblad form. This allows for minimizing negative terms, improving quantum trajectory simulations and GKSL equation approximations.
Area of Science:
- Quantum physics
- Open quantum systems
- Theoretical chemistry
Background:
- Time-local quantum master equations describe open quantum systems beyond ultraweak coupling.
- Standard Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form is often not applicable.
- Redfield and Hu-Paz-Zhang equations are prominent examples not in GKSL form.
Purpose of the Study:
- Demonstrate that Redfield and Hu-Paz-Zhang equations can be converted to a pseudo-Lindblad form.
- Investigate transformations that preserve the pseudo-Lindblad dissipator.
- Optimize negative term weights for improved numerical methods.
Main Methods:
- Mathematical transformation of quantum master equations.
- Analysis of dissipator properties under specific transformations.
- Investigation of pseudo-Lindblad equation unraveling and truncation.
Main Results:
- Both Redfield and Hu-Paz-Zhang equations can be cast into a pseudo-Lindblad form.
- Pseudo-Lindblad form features a GKSL-like dissipator with negative weights.
- Transformations exist that alter the balance of positive and negative weights.
Conclusions:
- The pseudo-Lindblad form offers a pathway to handle non-GKSL master equations.
- Minimizing negative terms is crucial for quantum trajectory convergence.
- Negative term truncation provides a route to approximate GKSL equations.
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