Boson Gas Mean Field Model Trapped by Weak Harmonic Potentials in Mesoscopic Scaling (Applications of Renormalization Group Methods in Mathematical Sciences)
Year: 2010
Type: article
Abstract: A model of a mean-field interacting boson gas trapped by a weak harmonic potential is considered by means of the theory of Random Point Field [RPF].In the previous work, the weak potential limit of the RPF which describes the position distribution of the constituent particles of the gas has been obtained.The limiting RPF concerns the distribution of the gas near the bottom of the harmonic potentials.In this note, we deal with the same model in the different scale to consider the large scale distribution of the system. §1. Introduction and Main ResultsWe consider the quantum statistical mechanical models of boson gas in \mathbb{R}^{d}(d> 2) equipped with a $\kappa$ -parameterized family of one-particle Hamiltonians of harmonic oscillators:(which are self-adjoint operators in the Hilbert space \mathfrak{H}:=L^{2}() .In this model, the limit $\kappa$\rightarrow\infty (weak harmonic limit [WHL]) can be considered as a kind of thermodynamic limit.In the previous paper [15], the position distribution of the constituent bosons of the model and its WHL is studied by means of random point
Author: Hiroshi Tamura
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1323953