Control of the symmetry breaking in double-well potentials by the resonant nonlinearity management

Nistazakis, H. E.; Malomed, Boris A.; Kevrekidis, P. G.; Frantzeskakis, D. J.

doi:10.1063/1.3559137

Cited by 1 publication

(4 citation statements)

References 74 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(8). On the other hand, at very small ε, the relevant ansatz is also different, as it amounts to soliton (22).…”

Section: The Variational Approximation (Va)mentioning

confidence: 99%

“…9, demonstrates that the variational ansatz predicts the solutions belonging to the top branch of the bifurcation diagram [see Fig. 8(a)] in a qualitatively correct form, while the solutions belonging to the bottom branch have no numerically found counterparts, being an artifact of the VA. On the other hand, it is relevant to stress that the other analytical approximation, based on soliton ansatz (22), (24), correctly demonstrates that the supercritical SSB bifurcation occurs at small ε too.…”

Section: Numerical Solutions Of Eqs (3) Andmentioning

confidence: 99%

“…The increase of ε leads to expansion of the stability range, which may be explained by dint of the following argument. In the case when both ε and N are large, the odd mode may be considered as a superposition of two narrow half-solitons (22), with norms N → N/2, opposite signs, and centers located at opposite points, ±ξ. Because the energy of the free soliton, determined by Eq.…”

Section: Excited Modesmentioning

confidence: 99%

“…[22], in the framework of a model which combines the DWP and "nonlinearity management", i.e., time-periodic modulation of coefficient g in Eq. (1).…”

Section: Introduction and The Modelmentioning

confidence: 99%

See 3 more Smart Citations

Spontaneous symmetry breaking in a split potential box

2016

View full text Add to dashboard Cite

We report results of the analysis of the spontaneous symmetry breaking (SSB) in the basic (actually, simplest) model which is capable to produce the SSB phenomenology in the one-dimensional setting. It is based on the Gross-Pitaevskii -nonlinear Schrödinger equation with the cubic selfattractive term and a double-well-potential built as an infinitely deep potential box split by a narrow (delta-functional) barrier. The barrier's strength, ε, is the single free parameter of the scaled form of the model. It may be implemented in atomic Bose-Einstein condensates and nonlinear optics. The SSB bifurcation of the symmetric ground state (GS) is predicted analytically in two limit cases, viz, for deep or weak splitting of the potential box by the barrier (ε ≫ 1 or ε ≪ 1, respectively). For the generic case, a variational approximation (VA) is elaborated. The analytical findings are presented along with systematic numerical results. Stability of stationary states is studied through the calculation of eigenvalues for small perturbations, and by means of direct simulations. The GS always undergoes the SSB bifurcation of the supercritical type, as predicted by the VA at moderate values of ε, although the VA fails at small ε, due to inapplicability of the underlying ansatz in that case. However, the latter case is correctly treated by the approximation based on a soliton ansatz. On top of the GS, the first and second excited states are studied too. The antisymmetric mode (the first excited state) is destabilized at a critical value of its norm. The second excited state undergoes the SSB bifurcation, like the GS, but, unlike it, the bifurcation produces an unstable asymmetric mode. All unstable modes tend to spontaneously reshape into the asymmetric GS.

show abstract

“…(8). On the other hand, at very small ε, the relevant ansatz is also different, as it amounts to soliton (22).…”

Section: The Variational Approximation (Va)mentioning

confidence: 99%

Section: Numerical Solutions Of Eqs (3) Andmentioning

confidence: 99%

Section: Excited Modesmentioning

confidence: 99%

“…[22], in the framework of a model which combines the DWP and "nonlinearity management", i.e., time-periodic modulation of coefficient g in Eq. (1).…”

Section: Introduction and The Modelmentioning

confidence: 99%

See 2 more Smart Citations