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arXiv · 1509.04631

Bogoliubov correction to the mean-field dynamics of interacting bosons

Phan Thành Nam·Marcin Napiórkowski
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Abstract

We consider the dynamics of a large quantum system of $N$ identical bosons in 3D interacting via a two-body potential of the form $N^{3β-1} w(N^β(x-y))$. For fixed $0\leq β<1/3$ and large $N$, we obtain a norm approximation to the many-body evolution in the $N$-particle Hilbert space. The leading order behaviour of the dynamics is determined by Hartree theory while the second order is given by Bogoliubov theory.

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Phan Thành Nam, Marcin Napiórkowski. 2017-08-26. Bogoliubov correction to the mean-field dynamics of interacting bosons. https://doi.org/10.4310/atmp.2017.v21.n3.a4

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