Coupled Oscillator systems for Microwave Applications: Optimized Design Based on the Study and Control of the Multiple Coexisting Solutions in Systems with Symmetry

Collado, Ana; Georgiadis, Apostolos

doi:10.1007/978-3-642-04227-0_12

Cited by 1 publication

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“…Arrays of coupled oscillators are ubiquitous in nature, and their oscillatory motions are usually applied in technological sciences [1][2][3][4][5]. Thanks to this, there has been an increasing interest in the dynamical and statistical behavior of a set of coupled oscillators so far.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Invariant Applied on General Time-Dependent Three Coupled Nano-Optomechanical Oscillators

Hassoul

Benseridi

Choi

2021

Journal of Nanomaterials

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A quadratic invariant operator for general time-dependent three coupled nano-optomechanical oscillators is investigated. We show that the invariant operator that we have established satisfies the Liouville-von Neumann equation and coincides with its classical counterpart. To diagonalize the invariant, we carry out a unitary transformation of it at first. From such a transformation, the quantal invariant operator reduces to an equal, but a simple one which corresponds to three coupled oscillators with time-dependent frequencies and unit masses. Finally, we diagonalize the matrix representation of the transformed invariant by using a unitary matrix. The diagonalized invariant is just the same as the Hamiltonian of three simple oscillators. Thanks to such a diagonalization, we can analyze various dynamical properties of the nano-optomechanical system. Quantum characteristics of the system are investigated as an example, by utilizing the diagonalized invariant. We derive not only the eigenfunctions of the invariant operator, but also the wave functions in the Fock state.

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