Biswas, Subhadip ; Bhattacharjee, Jayanta K. (2019) On the properties of a class of higher-order Mathieu equations originating from a parametric quantum oscillator Nonlinear Dynamics, 96 (1). pp. 737-750. ISSN 0924-090X
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Official URL: http://doi.org/10.1007/s11071-019-04818-9
Related URL: http://dx.doi.org/10.1007/s11071-019-04818-9
Abstract
Evolution in time of an arbitrary initial state for a parametrically driven quantum oscillator is an interesting problem since there exist regions in param- eter space (defined by the amplitude and frequency of the driving) where the moments of the probability dis- tribution can diverge in time. While the first moment satisfies a Mathieu equation, the higher-order moments follow Mathieu like equations of order greater than two. It is not very often that a physical problem gives rise to higher-order Mathieu equations. Hence, we give a detailed study of the different stability zones associ- ated with the parametric quantum oscillator, using per- turbative techniques traditionally associated with the Mathieu equation. We verify our results by numerical analysis, thus demonstrating that for the higher-order Mathieu equations, the traditional perturbation theory methods give a consistent account of the stability zones.
Item Type: | Article |
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Source: | Copyright of this article belongs to Springer-Verlag. |
ID Code: | 133807 |
Deposited On: | 30 Dec 2022 09:10 |
Last Modified: | 30 Dec 2022 09:10 |
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