EMS series of congress reports

Bogoliubov theory for many-body quantum systems

Benjamin Schlein

Published May 18, 2021• 0 citations

Abstract

We review some recent applications of rigorous Bogoliubov theory. We show how Bogoliubov theory can be used to approximate quantum fluctuations, both in the analysis of the energy spectrum and in the study of the dynamics of many-body quantum systems.

DOI: 10.4171/ecr/18-1/22

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EMS series of congress reports

Bogoliubov theory for many-body quantum systems

Benjamin Schlein

Published May 18, 2021• 0 citations

Publisher

Abstract

DOI: 10.4171/ecr/18-1/22

Related papers

Norm approximation for many-body quantum dynamics and Bogoliubov theory

Phan Thành Nam, Marcin Napiórkowski

We review some recent results on the norm approximation to the Schrödinger dynamics. We consider $N$ bosons in $\mathbb{R}^3$ with an interaction potential of the form $N^{3β-1}w(N^β(x-y))$ with $0\le β<1/2$ , and show that in the large $N$ limit, the fluctuations around the condensate can be effectively described using Bogoliubov approximation.We review some recent results on the norm approximation to the Schrödinger dynamics. We consider $N$ bosons in $\mathbb{R}^3$ with an interaction potential of the form $N^{3β-1}w(N^β(x-y))$ with $0\le β<1/2$, and show that in the large $N$ limit, the fluctuations around the condensate can be effectively described using Bogoliubov approximation.