Rotational Bose-Einstein condensates can exhibit quantized vortices as topological excitations.In this study,the ground and excited states of the rotational Bose-Einstein condensates are systematically studied by calc...Rotational Bose-Einstein condensates can exhibit quantized vortices as topological excitations.In this study,the ground and excited states of the rotational Bose-Einstein condensates are systematically studied by calculating the stationary points of the Gross-Pitaevskii energy functional.Various excited states and their connections at different rotational frequencies are revealed in solution landscapes constructed with the constrained high-index saddle dynamics method.Four excitation mechanisms are identified:vortex addition,rearrangement,merging,and splitting.We demonstrate changes in the ground state with increasing rotational frequencies and decipher the evolution of the stability of ground states.展开更多
We introduce a generalized numerical algorithm to construct the solution landscape,which is a pathway map consisting of all the stationary points and their connections.Based on the high-index optimizationbased shrinki...We introduce a generalized numerical algorithm to construct the solution landscape,which is a pathway map consisting of all the stationary points and their connections.Based on the high-index optimizationbased shrinking dimer(Hi OSD)method for gradient systems,a generalized high-index saddle dynamics(GHi SD)is proposed to compute any-index saddles of dynamical systems.Linear stability of the index-k saddle point can be proved for the GHi SD system.A combination of the downward search algorithm and the upward search algorithm is applied to systematically construct the solution landscape,which not only provides a powerful and efficient way to compute multiple solutions without tuning initial guesses,but also reveals the relationships between different solutions.Numerical examples,including a three-dimensional example and the phase field model,demonstrate the novel concept of the solution landscape by showing the connected pathway maps.展开更多
基金L.Z.is supported by the National Key Research and Development Program of China 2021YFF1200500 and the National Natural Science Foundation of China(No.12225102,T2321001,12050002,and 12288101)J.Y.is supported by the National Research Foundation,Singapore(Project No.NRF-NRFF13-2021-0005)+1 种基金Q.D.is supported by the National Science Foundation(DMS-2012562 and DMS-1937254)Y.C.is supported by the National Natural Science Foundation of China(No.12171041)。
文摘Rotational Bose-Einstein condensates can exhibit quantized vortices as topological excitations.In this study,the ground and excited states of the rotational Bose-Einstein condensates are systematically studied by calculating the stationary points of the Gross-Pitaevskii energy functional.Various excited states and their connections at different rotational frequencies are revealed in solution landscapes constructed with the constrained high-index saddle dynamics method.Four excitation mechanisms are identified:vortex addition,rearrangement,merging,and splitting.We demonstrate changes in the ground state with increasing rotational frequencies and decipher the evolution of the stability of ground states.
基金supported by National Natural Science Foundation of China(Grant No.11861130351)the support from the Elite Program of Computational and Applied Mathematics for Ph D Candidates of Peking University。
文摘We introduce a generalized numerical algorithm to construct the solution landscape,which is a pathway map consisting of all the stationary points and their connections.Based on the high-index optimizationbased shrinking dimer(Hi OSD)method for gradient systems,a generalized high-index saddle dynamics(GHi SD)is proposed to compute any-index saddles of dynamical systems.Linear stability of the index-k saddle point can be proved for the GHi SD system.A combination of the downward search algorithm and the upward search algorithm is applied to systematically construct the solution landscape,which not only provides a powerful and efficient way to compute multiple solutions without tuning initial guesses,but also reveals the relationships between different solutions.Numerical examples,including a three-dimensional example and the phase field model,demonstrate the novel concept of the solution landscape by showing the connected pathway maps.
