In this paper we consider a two-mode dynamical system as a model for a driven one-dimensional damped Bose–Einstein condensate in a double-well trapping potential. In the case of a constant external driving force the existence and stability of stationary solutions are discussed in relation to the values of the physical parameters. In the case of a time-dependent periodic external driving force the existence of limit cycles is proved, and the amplitude of these limit cycles exhibits a jump phenomenon for critical values of the physical parameters.
On a mathematical model for a damped and driven double-well Bose–Einstein condensate / Gavioli, A.; Sacchetti, A.. - In: PHYSICA D-NONLINEAR PHENOMENA. - ISSN 0167-2789. - 414:(2020), pp. 132711-132711. [10.1016/j.physd.2020.132711]
On a mathematical model for a damped and driven double-well Bose–Einstein condensate
Gavioli A.;Sacchetti A.
2020
Abstract
In this paper we consider a two-mode dynamical system as a model for a driven one-dimensional damped Bose–Einstein condensate in a double-well trapping potential. In the case of a constant external driving force the existence and stability of stationary solutions are discussed in relation to the values of the physical parameters. In the case of a time-dependent periodic external driving force the existence of limit cycles is proved, and the amplitude of these limit cycles exhibits a jump phenomenon for critical values of the physical parameters.
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