https://doi.org/10.1140/epjd/s10053-025-01070-2
Regular Article - Photons
Density matrix analysis of systems with periodic Hamiltonians
Department of Astrophysics and High Energy Physics, S. N. Bose National Centre for Basic Sciences, JD Block, Sector-III, 700 106, Salt Lake City, Kolkata, India
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Received:
15
July
2025
Accepted:
15
September
2025
Published online:
29
September
2025
In this work, we consider simple systems that are governed by Hamiltonians with time periodicity. Our analysis is mainly focused on the density matrix approach and aims to solve the von Neumann equation of motion from which one can extract the state of the system when the system is in a pure state. We start our analysis with the standard Rabi-oscillation problem. We consider a density matrix corresponding to the entire model system and solve the von Neumann equation of motion. We have then made use of the Lewis-Reisenfeld invariant approach and arrived at the exact same result, which implies that the density matrix of the system can indeed be identified with the Lewis invariant. Then, we consider a two-level system with a constant magnetic field in the z-direction and a time-dependent magnetic field in the x-direction. We solve the von Neumann equation of motion for this system and calculate the various coherence measures, and plot them to investigate the time dependence and reliability of different coherence measures.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
