Probability distributions in quantum statistical mechanics
type: Item
instance of: scholarly article
title: Probability distributions in quantum statistical mechanics
zbMATH Open document ID: 0565.60080
author: Mark Kon
published in: Lecture Notes in Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The monograph studies primarily probability distributions of observables associated to quantum statistical systems of noninteracting bosons and fermions as functions of the spectral measure of the Hamiltonians. In particular, the asymptotic behaviour for small energies of observables of the form \(\sum_{j}n_ jg(E_ j)\), where \(n_ j\) are occupation numbers on the canonical ensemble (the symmetric case being the nontrivial one), and \(\{E_ j\}\) the one-particle energy eigenvalues, is studied for several classes of Stieltjes-spectral measures dF (e.g., of the form \(F(E)=bE\) or \(F(E)=bE^ 2\), with b constant). Both Minkowski and Einstein space \(S^ 3\times {\mathbb{R}}\) are considered, the latter being connected to an interesting application to cosmology which underlies the physical motivation; cf. \textit{H. P. Jakobsen}, \textit{M. Kon} and \textit{I. E. Segal}, Phys. Rev. Lett. 42, 1788-1791 (1979). The basic formalism is a proper definition of ''integrals'' of independent random variables w.r.t. the appropriate spectral measures; depending on the latter several more or less ''singular'' central limit theorems are proved.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B10
Mathematics Subject Classification ID: 60-02
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 3901788
zbMATH Keywords: quantum statistical systems
zbMATH Keywords: asymptotic behaviour for small energies
zbMATH Keywords: Stieltjes-spectral measures
zbMATH Keywords: central limit theorems
reviewed by: Walter F. Wreszinski
MaRDI profile type: Publication
DOI: 10.1007/BFB0077154
description: scientific article; zbMATH DE number 3901788