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Physica A Statistical Mechanics and its Applications

Quantum dynamics for general time-dependent three coupled oscillators based on an exact decoupling

Sara Hassoul, Salah Menouar, Hamid Benseridi, Jeong Ryeol Choi

Published Jun 17, 2022• 2 citations
Publisher
DOI
10.1016/j.physa.2022.127755

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In a recent paper, Hassoul et al.[1], the authors proposed an analysis of the quantum dynamics for general time-dependent three coupled oscillators through an approach based on their decouplement using the unitary transformation method. Thus, to diagonalize the transformed Hamiltonian, they introduce a new unitary operator corresponding to a three-dimensional rotation parameterized by Euler angles. Through this procedure, Hassoul et al. [1] claim that the coupled oscillatory subsystems are completely decoupled. This last approach is partly wrong. In this brief note, we show that their method is indeed not correct and we try to explain what truly lies behind their mistakes. We also propose a brief discussion on an alternative method that might achieve satisfactory results.

arXiv:2209.11560•Sep 23, 2022•0 citations

General solution for multi-dimensional time-dependent coupled quantum oscillator

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By using the Lewis–Riesenfeld invariants theory, we investigate the quantum dynamics of a two-dimensional (2D) time-dependent coupled oscillator. We introduce a unitary transformation and show the conditions under which the invariant operator is uncoupled to describe two simple harmonic oscillators with time-independent frequencies and unit masses. The decouplement allows us to easily obtain the corresponding eigenstates. The generalization to three-dimensional (3D) time-dependent coupled oscillator is briefly discussed where a diagonalized invariant, which is exactly the sum of three simple harmonic oscillators, is obtained under specific conditions on the parameters.
In a recent paper, Hassoul et al.[1], the authors proposed an analysis of the quantum dynamics for general time-dependent three coupled oscillators through an approach based on their decouplement using the unitary transformation method. Thus, to diagonalize the transformed Hamiltonian, they introduce a new unitary operator corresponding to a three-dimensional rotation parameterized by Euler angles. Through this procedure, Hassoul et al. [1] claim that the coupled oscillatory subsystems are completely decoupled. This last approach is partly wrong. In this brief note, we show that their method is indeed not correct and we try to explain what truly lies behind their mistakes. We also propose a brief discussion on an alternative method that might achieve satisfactory results.