Monotonicity of quantum ground state energies: Bosonic atoms and stars
type: Item
instance of: scholarly article
title: Monotonicity of quantum ground state energies: Bosonic atoms and stars
zbMATH Open document ID: 1188.82046
published in: Journal of Statistical Physics
publication date: 2010-02-15T00:00:00Z
full work available at URL: https://arxiv.org/abs/1001.4280
review text: For quantum \(N\)-body systems the non-relativistic bosonic ground state energy \(E^B(N)\) is studied with either Coulomb or Newton interaction. The Coulomb system are bosonic atoms with fixed nucleus, the quantity \(E^B_C(N)/P_C(N)\) grows monotonically with \(N>1\), where \(P_C(N)= N^2(N- 1)\). The Newton systems are bosonic stars. It is shown that when the bosons are centrally attracted to a fixed gravitational grain of mass \(M>0\) and \(N>2\), then \(E_N^B(N,M)/P_N(N)\) grows monotonically with \(N\), where \(P_N(N)= N(N- 1)(N- 2)\). In the translation invariant problem -- \((M= 0)\) -- it is shown that for \(N>1\) the quantity \(E^B_N(N; 0)/P_C(N)\) grows monotonically with \(N\), here \(P_C(N)\) is the expression for the Coulomb problem. The applications of the new monotonicity results are discussed.
Mathematics Subject Classification ID: 82C22
Mathematics Subject Classification ID: 81V70
zbMATH DE Number: 5671563
zbMATH Keywords: non-relativistic quantum mechanics
zbMATH Keywords: \(N\) body problems
zbMATH Keywords: ground state energies
zbMATH Keywords: bosonic atoms
zbMATH Keywords: bosonic stars
zbMATH Keywords: rigorous results
author: Michael K.-H. Kiessling
reviewed by: Iván Abonyi
MaRDI profile type: Publication
OpenAlex ID: W3101253452
arXiv ID: 1001.4280
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DOI: 10.1007/S10955-009-9843-9
description: scientific article