On the nature of the lowest state of a Bose crystal

TL;DR

This paper demonstrates that the ground state of a Bose crystal must have a nodal wave function, implying it cannot be a simple non-degenerate state, and proposes an ansatz with potential experimental implications.

Contribution

It provides a quantum mechanical proof that the lowest state of a Bose crystal involves a wave function with nodes, challenging previous assumptions about its nature.

Findings

Ground state of Bose systems is isotropic and non-degenerate.

Lowest state of a Bose crystal must have a wave function with nodes.

Proposes an ansatz for the wave function of a 3D Bose crystal.

Abstract

As is known, the ground state (GS) of a system of spinless bosons must be non-degenerate and must be described by a nodeless wave function. With the help of the general quantum mechanical analysis we show that any \textit{anisotropic} state of a system of spinless bosons is degenerate. We prove this for a two-dimensional (2D) system, infinite or finite circular, and for a three-dimensional (3D) system, infinite or finite ball-shaped. It is natural to expect that this is valid for finite 2D and 3D systems of any shape. Hence, GS of a Bose system of any density is isotropic and, therefore, corresponds to a liquid or gas. Therefore, the lowest state of a 2D or 3D natural crystal consisting of spinless bosons should be described by a wave function with nodes. This leads to nontrivial experimental predictions. We propose a possible ansatz for the wave function of the lowest state of a 3D Bose crystal and discuss possible experimental consequences.