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数理解析研究所講究録

A Gibbs Theory for States of Boson Systems(Recent Trends in Infinite Dimensional Non-Commutative Analysis)

Volkmar Liebscher

Published Apr 1, 1998• 0 citations
OpenAlex

Abstract

Based on certain conditional expectations leading to conditional local states we provide a Gibbs Theory analogous to $[20, 21]$ .As example, we look at specifications corresponding to coherent states and the ideal Bose gas.

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arXiv:2010.04070•Oct 8, 2020•1 citation
Based on certain conditional expectations leading to conditional local states we provide a Gibbs Theory analogous to [20,21][20, 21][20,21] .As example, we look at specifications corresponding to coherent states and the ideal Bose gas.
It is usually assumed that the Bose crystal at T=0T=0T=0 corresponds to the genuine ground state of a Bose system, i.e., this state is non-degenerate and is described by the wave function without nodes. By means of symmetry analysis we show that the ground state of a Bose system of any density should correspond to a liquid or gas, but not to a crystal. The main point is that any anisotropic state of a system of spinless bosons is degenerate. We prove this for an infinite three-dimensional (3D) system and a finite ball-shaped 3D system. One can expect that it is true also for a finite system of any form. Therefore, the anisotropic state cannot be the genuine ground state. Hence, a zero-temperature natural 3D crystal should correspond to an excited state of a Bose system. The wave function Ψ0cΨ^{c}_{0}Ψ0c​ of a zero-temperature 3D Bose crystal is proposed for zero boundary conditions. Apparently, such Ψ0cΨ^{c}_{0}Ψ0c​ corresponds to a local minimum of energy (absolute minimum corresponds to a liquid). Those properties yield the possibility of existence of superfluid liquid H2_{2}2​, Ne, Ar, and other inert elements. We propose several possible experimental ways of obtaining them.