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An operational perspective on the Magnus-Fer conundrum in time-dependent quantum mechanics
Kuntal Mukherjee1, Shreyan Ganguly1, Ramesh Ramachandran1
1Department of Chemical Sciences Indian Institute of Science Education and Research (IISER), Mohali, Sector 81, Manauli P.O. Box, 140306 Mohali, Punjab, India.
The Journal of Chemical Physics
|April 2, 2025
Summary
This study compares the Magnus expansion (ME) and Fer expansion (FE) for analyzing quantum systems with periodic Hamiltonians. It details their operational advantages and disadvantages for spectroscopy and chemical physics applications.
Area of Science:
- Quantum mechanics
- Chemical physics
- Spectroscopy
Background:
- Analytic methods are crucial for understanding quantum systems driven by periodic Hamiltonians.
- The Magnus expansion (ME) and Fer expansion (FE) are key theoretical frameworks for time-evolution studies.
- Operational aspects and exactness in replicating experimental results determine the success of analytic methods.
Purpose of the Study:
- To analyze the operational advantages and disadvantages of the Magnus expansion (ME) versus the Fer expansion (FE) for periodic Hamiltonians.
- To compare the relative merits and demerits of these two analytic schemes.
- To discuss the long-term and short-term behavior of both methods in experimentally verifiable systems.
Main Methods:
- Analysis of analytic methods for quantum systems with periodic Hamiltonians.
- Comparison of the Magnus expansion (ME) and Fer expansion (FE) schemes.
- Examination of operational aspects and theoretical exactness.
Main Results:
- The study provides an in-depth analysis of the operational aspects of ME and FE schemes.
- Relative merits and demerits of both methods are discussed for periodic Hamiltonians.
- Analytic expressions are derived to discuss the long-term/short-term behavior.
Conclusions:
- The Fer expansion (FE) offers operational advantages over the Magnus expansion (ME) in certain applications.
- Both methods have distinct merits and demerits depending on the specific problem in quantum dynamics.
- Further research can validate these findings in experimentally verifiable systems.
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