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Simulating a Quantum Composite System by Coupled Classical Oscillators

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Abstract

It is known that the adiabatic evolution and Berry phase of a quantum can be mapped into the classical dynamics and Hannay’s angle of coupled oscillators in a strictly mathematical way. In this work, we show that a quantum composite system consisting of two spin-1/2 can also be mapped into coupled two sets of classical oscillators by using this quantum-classical mapping. The evolution and geometric phase for the quantum composite system have been mapped into the classical dynamics and Hannay’s angle for the oscillators. The quantum entanglement has also been mapped into the correlation between the two sets of coupled oscillators. We also provide a way to study the classical geometric angle by mapping the geometric phases for the quantum subsystems into classical ones. Our results can provide a new way to simulate the quantum composite system and study the classical composite system.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (11747155), Science and Technology Foundation of Education Department of Jilin Province of China (JJKH20181162KJ).

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  1. International Education Teachers School, Changchun Normal University, Changchun, 130024, China

    Jing Yang

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Yang, J. Simulating a Quantum Composite System by Coupled Classical Oscillators. Int J Theor Phys 62, 45 (2023). https://doi.org/10.1007/s10773-023-05311-1

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