Can a crystal be the ground state of a Bose system?
Abstract
It is usually assumed that the Bose crystal at 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 of a zero-temperature 3D Bose crystal is proposed for zero boundary conditions. Apparently, such corresponds to a local minimum of energy (absolute minimum corresponds to a liquid). Those properties yield the possibility of existence of superfluid liquid H, Ne, Ar, and other inert elements. We propose several possible experimental ways of obtaining them.
Cite
@article{arxiv.2010.04070,
title = {Can a crystal be the ground state of a Bose system?},
author = {Maksim D. Tomchenko},
journal= {arXiv preprint arXiv:2010.04070},
year = {2021}
}
Comments
39 one-column pages, 2 figures; v2: Section 2, Appendices 1 and 3, and references are revised, Appendix 2 is added