THREE-BODY INTERACTIONS BEYOND THE GROSS–PITAEVSKII EQUATION AND MODULATIONAL INSTABILITY OF BOSE–EINSTEIN CONDENSATES

2012 ◽  
Vol 26 (32) ◽  
pp. 1250202 ◽  
Author(s):  
DIDIER BELOBO BELOBO ◽  
GERMAIN HUBERT BEN-BOLIE ◽  
TIMOLEON CREPIN KOFANE
Keyword(s):  
Modulational Instability ◽  
Mean Field Theory ◽  
Mean Field ◽  
External Potential ◽  
Pitaevskii Equation ◽  
Theoretical Predictions ◽  
The Mean ◽  
Three Body ◽  
Bose Einstein ◽  
Condensate System

Beyond the mean-field theory, a new model of the Gross–Pitaevskii equation (GPE) that describes the dynamics of Bose–Einstein condensates (BECs) is derived using an appropriate phase-imprint on the old wavefunction. This modified version of the GPE in addition to the two-body interactions term, also takes into account effects of the three-body interactions. The three-body interactions consist of a quintic term and the delayed nonlinear response of the condensate system term. Then, the modulational instability (MI) of the new GPE confined in an attractive harmonic potential is investigated. The analytical study shows that the three-body interactions destabilize more the condensate system while the external potential alleviates the instability. Numerical results confirm the theoretical predictions. Further numerical investigations of the behavior of solitons reveal that the three-body interactions enhance the appearance of solitons, increase the number of solitons generated and deeply change the lifetime of solitons. Moreover, the external potential delays the appearance of solitons. Besides, a new initial condition is introduced which enables to increase the number of solitons created and deeply affects the trail of chains of solitons generated. Moreover, the MI of a condensate without the external potential, and in a repulsive potential is also investigated.

scholarly journals PATTERN FORMING DYNAMICAL INSTABILITIES OF BOSE–EINSTEIN CONDENSATES

2004 ◽  
Vol 18 (05n06) ◽  
pp. 173-202 ◽  
Author(s):  
P. G. KEVREKIDIS ◽  
D. J. FRANTZESKAKIS
Keyword(s):  
Modulational Instability ◽  
Mean Field ◽  
Three Dimensional ◽  
Two Dimensions ◽  
One Dimension ◽  
Pitaevskii Equation ◽  
Long Wavelength ◽  
Pattern Forming ◽  
Bose Einstein ◽  
Dynamical Instabilities

In this short topical review, we revisit a number of works on the pattern-forming dynamical instabilities of Bose–Einstein condensates in one- and two-dimensional settings. In particular, we illustrate the trapping conditions that allow the reduction of the three-dimensional, mean field description of the condensates (through the Gross–Pitaevskii equation) to such lower dimensional settings, as well as to lattice settings. We then go on to study the modulational instability in one dimension and the snaking/transverse instability in two dimensions as typical examples of long-wavelength perturbations that can destabilize the condensates and lead to the formation of patterns of coherent structures in them. Trains of solitons in one dimension and vortex arrays in two dimensions are prototypical examples of the resulting nonlinear waveforms, upon which we briefly touch at the end of this review.

Effects of three-body interactions on the instabilities and self-oscillations of the four-wave mixing in Bose–Einstein condensates

2017 ◽  
Vol 31 (21) ◽  
pp. 1750150 ◽  
Author(s):  
G. J. Ngounga Makoundit ◽  
T. B. Ekogo ◽  
A. B. Moubissi ◽  
G. H. Ben-Bolie ◽  
T. C. Kofane
Keyword(s):  
Probe Beam ◽  
Mean Field ◽  
Field Approximation ◽  
Four Wave Mixing ◽  
Signal Beam ◽  
Mean Field Approximation ◽  
Pitaevskii Equation ◽  
Wave Mixing ◽  
Three Body ◽  
Bose Einstein

In this paper, we analyze and discuss instabilities and self-oscillations of four-wave mixing in two-component Bose–Einstein condensates with two- and three-body interatomic interactions. The model is very accurately described in the mean-field approximation by the cubic–quintic Gross–Pitaevskii equation. The relation between the input and output field intensities is multivalued and the effects of the quintic nonlinearity on the self-oscillations of the system are studied. We have also found that the magnitude of the signal beam increases with the increase of the intensity of the probe beam, up to a saturated value, then it decreases with the increase of the intensity of the probe beam. We have shown that the three-body interatomic interactions enhance this saturated value.

Stability of binary condensates with spatial modulations of quintic nonlinearities in optical lattices

2015 ◽  
Vol 29 (03) ◽  
pp. 1550008 ◽  
Author(s):  
M. D. Mboumba ◽  
A. B. Moubissi ◽  
T. B. Ekogo ◽  
D. Belobo Belobo ◽  
G. H. Ben-Bolie ◽  
...  
Keyword(s):  
Optical Lattice ◽  
Optical Lattices ◽  
Mean Field ◽  
Collective Excitations ◽  
Pitaevskii Equation ◽  
Dependent Potential ◽  
The Mean ◽  
The Stability ◽  
Bose Einstein ◽  
Spatial Modulations

The stability and collective excitations of binary Bose–Einstein condensates with cubic and quintic nonlinearities in variable anharmonic optical lattices are investigated. By using the variational approach, the influences of the quintic nonlinearities and the shape of the external potential on the stability are discussed in details. It is found that the quintic intraspecies and interspecies interatomic interactions profoundly affect the stability criterion and collective excitations of the system. The shape dependent potential form that characterizes the optical lattice deeply alters the stability regions. Direct numerical simulations of the mean-field coupled Gross–Pitaevskii equation describing the system agree well with the analytical predictions.

scholarly journals Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Models ◽  
Classical Spin ◽  
The Mean ◽  
Classical Spin Models

scholarly journals RELATIVE MOTION CORRECTION TO FISSION BARRIERS

2008 ◽  
Vol 17 (01) ◽  
pp. 151-159 ◽  
Author(s):  
J. SKALSKI
Keyword(s):  
Relative Motion ◽  
Cluster Model ◽  
Motion Correction ◽  
Mean Field Theory ◽  
Mean Field ◽  
Ternary Fission ◽  
Skyrme Interaction ◽  
Hartree Fock ◽  
Fission Barriers ◽  
The Mean

We discuss the effect of kinetic energy of the relative motion becoming spurious for separate fragments on the selfconsistent mean-field fission barriers. The treatment of the relative motion in the cluster model is contrasted with the necessity of a simpler and approximate approach in the mean-field theory. A scheme of the energy correction to the Hartree-Fock is proposed. The results obtained with the effective Skyrme interaction SLy 6 show that the correction, previously estimated as ~ 8 MeV in A = 70 - 100 nuclei, amounts to 4 MeV in the medium heavy nucleus 198 Hg and to null in 238 U . However, the corrected barrier implies a shorter fission half-life of the latter nucleus. The same effect is expected to lower barriers for multipartition (i.e. ternary fission, etc) and make hyperdeformed minima less stable.

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