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Lecture notes series, Institute For Mathematical Sciences

Mathematical Theory and Numerical Methods for Bose-Einstein Condensation with Higher-Order Interaction

Yongyong Cai, Xinran Ruan

Published Jan 30, 2023• 0 citations
Publisher
DOI
10.1142/9789811266058_0003

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Abstract So far, attractive , trapless Bose–Einstein condensate (BEC) has been stabilized by considering the temporal modulation of the scattering length. However, there is no scope to stabilize the repulsive , trapless BEC even in the presence of the temporal modulation of the two-body interaction. However, in the present study, we stabilize the repulsive , trapless BEC by incorporating higher-order interaction. We also discuss the possibilities of the stabilization of repulsive, trapless BEC in the presence of time-varying higher-order interaction. Additionally, we verify our analytical findings by direct numerical simulation using the split-step Crank-Nicholson method.
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We investigate the modulational instability (MI) of trapped Bose–Einstein condensates with three-body and higher-order interactions employing both semi-analytical and numerical methods. Using the time-dependent variational approach, we derive variational equations for the time evolution of the amplitude, phase of modulational perturbation, and effective potential of the system. By means of an effective potential, we retrieve the corresponding MI condition of the dynamical system under consideration. The interplay between three-body interaction and higher-order interaction is discussed in detail. The semi-analytical predictions are confirmed through numerical simulations.