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The Ground State Energy of a Dilute Bose Gas in Dimension n >3

Aaen, Anders

arXiv.org, 2014-03

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Título:
The Ground State Energy of a Dilute Bose Gas in Dimension n >3
Autor: Aaen, Anders
Assuntos: Ground state ; Mathematics - Mathematical Physics ; Physics - Mathematical Physics ; Upper bounds
É parte de: arXiv.org, 2014-03
Descrição: We consider a Bose gas in spatial dimension \(n>3\) with a repulsive, radially symmetric two-body potential \(V\). In the limit of low density \(\rho\), the ground state energy per particle in the thermodynamic limit is shown to be \((n-2)|\mathbb S^{n-1}|a^{n-2}\rho\), where \(|\mathbb S^{n-1}|\) denotes the surface measure of the unit sphere in \(\mathbb{R}^n\) and \(a\) is the scattering length of \(V\). Furthermore, for smooth and compactly supported two-body potentials, we derive upper bounds to the ground state energy with a correction term \((1+C\gamma)8\pi^4a^6\rho^2|\ln(a^4\rho)|\) in dimension \(n=4\), where \(\gamma:=\int V(x)|x|^{-2}\, dx\), and a correction term which is \(\mathcal{O}(\rho^2)\) in higher dimensions.
Editor: Ithaca: Cornell University Library, arXiv.org
Idioma: Inglês

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