There are three main problems in the weakly nonlinear theory of hydrodynamic stability:(1)The ra- dius of convergence with respect to the perturbation parameter is too small and there is no concrete estimation for it....There are three main problems in the weakly nonlinear theory of hydrodynamic stability:(1)The ra- dius of convergence with respect to the perturbation parameter is too small and there is no concrete estimation for it.(2)The solution has a special structure, thus in general, it can not satisfy the initial condition posed by many practical problems.(3) When the linear part of its solution does not correspond to a neutral case. there are more than one way in determining the Landau constants, and practically no one knows which is the best way. In this paper, problems(1)and(2)are solved theoretically, and ways for its improvement have been proposed. By comparing the theoretical results with those obtained by numerical simulations, problem(3)has also been clari- fied.展开更多
Dimensionality is a central concept in developing the theory of low-dimensional physics.However,previous research on dimensional crossover in the context of a Bose-Einstein condensate(BEC)has focused on the single-com...Dimensionality is a central concept in developing the theory of low-dimensional physics.However,previous research on dimensional crossover in the context of a Bose-Einstein condensate(BEC)has focused on the single-component BEC.To our best knowledge,further consideration of the two-component internal degrees of freedom on the effects of dimensional crossover is still lacking.In this work,we are motivated to investigate the dimensional crossover in a three-dimensional(3D)Rabi-coupled two-component BEC.The spin degrees of freedom consist of the Rabi-like and inter-and intra-interaction coupling constants.The dimensional crossovers from 3D to 2D or 1D are controlled by the continuous increase of 1D or 2D lattice depth respectively.Then we analyze how the dimensionality of the model system combined with spin degrees of freedom can affect quantum fluctuations.Accordingly,the analytical expressions of the ground-state energy and quantum depletion of the system are obtained.Our results show that the dimensional crossover induces a characteristic 3D to quasi-2D or 1D crossover in the behavior of quantum fluctuations,with an emphasis on the separated effects of Rabi-like and inter-and intra-interaction coupling constants on the quantum fluctuations.Conditions for possible experimental realization of our scenario are also discussed.展开更多
In this paper,we study the higher genus FJRW theory of Fermat cubic singularity with maximal group of diagonal symmetries using Giventai formalism.As results,we prove the finite generation property and holomorphic ano...In this paper,we study the higher genus FJRW theory of Fermat cubic singularity with maximal group of diagonal symmetries using Giventai formalism.As results,we prove the finite generation property and holomorphic anomaly equation for the associated FJRW theory.Via general LG-LG mirror theorem,our results also hold for the Saito-Givental theory of the Fermat cubic singularity.展开更多
基金Project supported by the National Natural Science Foundation of China
文摘There are three main problems in the weakly nonlinear theory of hydrodynamic stability:(1)The ra- dius of convergence with respect to the perturbation parameter is too small and there is no concrete estimation for it.(2)The solution has a special structure, thus in general, it can not satisfy the initial condition posed by many practical problems.(3) When the linear part of its solution does not correspond to a neutral case. there are more than one way in determining the Landau constants, and practically no one knows which is the best way. In this paper, problems(1)and(2)are solved theoretically, and ways for its improvement have been proposed. By comparing the theoretical results with those obtained by numerical simulations, problem(3)has also been clari- fied.
基金supported by the Zhejiang Provincial Natural Science Foundation(Grant Nos.LZ21A040001 and LQ20A040004)the National Natural Science Foundation of China(Nos.12074344,and 12104407)the key projects of the Natural Science Foundation of China(Grant No.11835011).
文摘Dimensionality is a central concept in developing the theory of low-dimensional physics.However,previous research on dimensional crossover in the context of a Bose-Einstein condensate(BEC)has focused on the single-component BEC.To our best knowledge,further consideration of the two-component internal degrees of freedom on the effects of dimensional crossover is still lacking.In this work,we are motivated to investigate the dimensional crossover in a three-dimensional(3D)Rabi-coupled two-component BEC.The spin degrees of freedom consist of the Rabi-like and inter-and intra-interaction coupling constants.The dimensional crossovers from 3D to 2D or 1D are controlled by the continuous increase of 1D or 2D lattice depth respectively.Then we analyze how the dimensionality of the model system combined with spin degrees of freedom can affect quantum fluctuations.Accordingly,the analytical expressions of the ground-state energy and quantum depletion of the system are obtained.Our results show that the dimensional crossover induces a characteristic 3D to quasi-2D or 1D crossover in the behavior of quantum fluctuations,with an emphasis on the separated effects of Rabi-like and inter-and intra-interaction coupling constants on the quantum fluctuations.Conditions for possible experimental realization of our scenario are also discussed.
基金Supported by National Science Foundation of China(Grant No.11601279)National Science Foundation of China(Grant No.12071255)。
文摘In this paper,we study the higher genus FJRW theory of Fermat cubic singularity with maximal group of diagonal symmetries using Giventai formalism.As results,we prove the finite generation property and holomorphic anomaly equation for the associated FJRW theory.Via general LG-LG mirror theorem,our results also hold for the Saito-Givental theory of the Fermat cubic singularity.
