数学科学研究所
Insitute of Mathematical Science

Seminar :Quantitative Derivation of the Two-Component Gross–Pitaevskii Equation with Uniform-in-Time Convergence Rate

Seminar| Institute of Mathematical Sciences

Time: Friday, March 28th, 2025,14:30-15:30

LocationIMS, RS408

Speaker:Hongchao Zhang, Peking University

Abstract: We derive the time-dependent two-component Gross–Pitaevskii equation as an effective description of the dynamics of a dilute two-component Bose gas near its ground state, which exhibits a two-component Bose–Einstein condensate, in the Gross–Pitaevskii limit. Our main result establishes a uniform-in-time bound on the convergence rate between the many-body dynamics and the effective description, explicitly quantified in terms of the particle number N, and also implies a uniform-in-time bound for the one-component case. This improves upon the works of Michelangeli and Olgliati [2, 3] by providing a sharper, N-dependent, timeindependent convergence rate. Our approach further extends the framework of Benedikter, de Oliveira, and Schlein [1] to the multi-component Bose gas setting. More specifically, we develop the necessary Bogoliubov theory to analyze the dynamics of multi-component Bose gases in the Gross–Pitaevskii regime.


The talk is based on our recent work arXiv:2501.18787. This is joint work with Jinyeop Lee and Zhiwei Sun.

References

[1] N. Benedikter, G. de Oliveira, and B. Schlein. Quantitative derivation of the Gross–Pitaevskii equation. Commun. Pure Appl. Math., 68(8):1399–1482, 2015.

[2] A. Michelangeli and A. Olgiati. Gross–Pitaevskii non-linear dynamics for pseudo-spinor condensates. J. Nonlinear Math. Phys., 24(3):466–464, 2017.

[3] A. Olgiati. Effective Non-linear Dynamics of Binary Condensates and Open Problems, pages 239–256. Springer International Publishing, Cham, 2017.


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