Uniform in $N$ Global Well-posedness of the Time-Dependent Hartree-Fock-Bogoliubov Equations in ${\mathbb{R}}^{1+1}$

Abstract

In this article, we prove the global well-posedness of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations in ${\mathbb{R}}^{1+1}$ with two-body interaction potentials of the form $N^{-1}{v}_N(x)=N^{\beta -1}v(N^{\beta }x)$ where $v$ is a sufficiently regular radial function $v\in L^1(\mathbb{R})\cap C^{\infty }(\mathbb{R})$. In particular, using methods of dispersive PDEs similar to the ones used in Grillakis and Machedon, Comm. PDEs., (2017), we are able to show for any scaling parameter $\beta >0$ the TDHFB equations are globally well-posed in some Strichartz-type spaces independent of $N$, cf. (Bach et al. in arXiv:1602.05171).

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Cited by in corpus (1)

• On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate