Volume 60, Issue 334, January - April 2024

Proving the accuracy of invariant operator approach for quantum solutions of time-dependent coupled oscillators including relevant criticisms and perspectives

Ji Nny Song^♦

School of Electronic Engineering, Kyonggi University, Yeongtonggu, Suwon, Gyeonggi-do 16227, Republic of Korea

^♦Corresponding author
School of Electronic Engineering, Kyonggi University, Yeongtonggu, Suwon, Gyeonggi-do 16227, Republic of Korea

ABSTRACT

Choi recently published a research paper on the subject of quantizing general timedependent coupled oscillators (arXiv:2210.07551v1 [quant-ph] (2022)) using the invariant operator approach. In the present research, we provide a direct method for proving the correctness of such an invariant approach, together with relevant perspectives and criticisms. The difference of our method from Choi’s one in this context is that, while Choi managed the quantum system with the aid of the unitary transformation technique, we do not use such an auxiliary tool in our proof of accuracy. This demonstration may provide a definite mathematical testimony for the usefulness of adopting invariant operator approach in a straightforward way. Our proof is crucial in unfolding quantum information theory including optoelectromechanics via coupled devices which operate through electro-mechanical oscillations. We also discuss the consequences of Choi’s work and Zerimeche et al.’s works (Mod. Phys. Lett. B 37, 2250222 (2023) and others) which share many concepts with each other, including the relation between them.

Keywords: Coupled oscillators, Quantum dynamics, Unitary transformation, Quantum solutions, Invariant operator

Discovery, 2024, 60, e12d1423

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DOI: https://doi.org/10.54905/disssi.v60i334.e12d1423

Published: 23 March 2024