The SU(2)(+)h(4) Hamiltonian

Cheng, C M; Fung, P. C. W.

doi:10.1088/0305-4470/23/1/014

Cited by 4 publications

(5 citation statements)

References 18 publications

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“…The Lie transformation method can easily discriminate the classical resonance from a quantum one to reveal that the classical resonance is governed by the dynamical equations of Eq. (21) or Eq. ( 25) which only introduces an overall translation of the wave packet, while the quantum resonance induces quantum transitions between different internal states which dramatically modify the shape of the wave packet.…”

Section: Discussionmentioning

confidence: 99%

“…We consider for simplicity the one-dimensional model and a d-dimensional generalization is theoretically straightforward [19]. Totally, this Hamiltonian owns a well known real symplectic group of Sp(2d, R) [20] and we will consider it in a decomposed space with a Lie algebraic structure of su(2) h(4) [21]. Therefore six independent generators can be separately defined by [22] Then the Hamiltonian can be written as…”

Section: B Lie Transformation Methods On Ddpomentioning

confidence: 99%

“…The above time-dependent Hamiltonian has been extensively studied [16,23] and we will follow the algebraic method firstly proposed by Wei and Norman [21,24] and, recently, summarized in Ref. [25].…”

Section: B Lie Transformation Methods On Ddpomentioning

confidence: 99%

“…Now we give the main idea of the Lie transformation method [21] to solve or control the general quadratic Hamiltonian of Eq. ( 13) by adopting proper transformation parameters.…”

Section: Time-dependent Transformations On Lie Algebramentioning

confidence: 99%

“…Then the transformation of Û (t) can be a combination of the above six operators in a specific order. For simplicity, we choose the following successive transformations separated by h(4) algebra and su(2) algebra as [21]…”

Section: Time-dependent Transformations On Lie Algebramentioning

confidence: 99%

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Lie transformation method on quantum state evolution of a general time-dependent driven and damped parametric oscillator

Zhang

2016

Annals of Physics

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A variety of dynamics in nature and society can be approximately treated as a driven and damped parametric oscillator. An intensive investigation of this time-dependent model from an algebraic point of view provides a consistent method to resolve the classical dynamics and the quantum evolution in order to understand the time-dependent phenomena that occur not only in the macroscopic classical scale for the synchronized behaviors but also in the microscopic quantum scale for a coherent state evolution. By using a Floquet U-transformation on a general time-dependent quadratic Hamiltonian, we exactly solve the dynamic behaviors of a driven and damped parametric oscillator to obtain the optimal solutions by means of invariant parameters of Ks to combine with Lewis-Riesenfeld invariant method. This approach can discriminate the external dynamics from the internal evolution of a wave packet by producing independent parametric equations that dramatically facilitate the parametric control on the quantum state evolution in a dissipative system. In order to show the advantages of this method, several time-dependent models proposed in the quantum control field are analyzed in details.

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Section: Discussionmentioning

confidence: 99%

Section: B Lie Transformation Methods On Ddpomentioning

confidence: 99%

Section: B Lie Transformation Methods On Ddpomentioning

confidence: 99%

“…Now we give the main idea of the Lie transformation method [21] to solve or control the general quadratic Hamiltonian of Eq. ( 13) by adopting proper transformation parameters.…”

Section: Time-dependent Transformations On Lie Algebramentioning

confidence: 99%

Section: Time-dependent Transformations On Lie Algebramentioning

confidence: 99%

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