Bose crystal as a standing sound wave

TL;DR

This paper proposes that Bose crystals with simple cubic lattices are formed by standing sound waves, revealing a condensate of atoms and explaining nonclassical inertia moments observed in helium-4 crystals.

Contribution

It introduces a new wave function description for Bose crystals, showing they are formed by standing sound waves and contain a condensate of atoms at specific wave vectors.

Findings

Bose crystal ground state described by standing sound waves.

Existence of atomic condensate at specific wave vectors.

Explanation of nonclassical inertia moments in helium-4.

Abstract

A new class of solutions for Bose crystals with a simple cubic lattice consisting of N atoms is found. The wave function (WF) of the ground state takes the form \Psi_0=e^{S_{w}^{l}+S_{b}}*\prod_j [\sin{k_{l_x}x_{j}}\sin{k_{l_y}y_{j}}\sin{k_{l_z}z_{j}}], where e^{S_{b}} is the ground-state WF of a fluid, and \textbf{k}_l=(\pi/a_l, \pi/a_l, \pi/a_l) (a_l is the lattice constant). The state with a single longitudinal acoustic phonon is described by the WF \Psi_k=[\rho_{-k}+corrections + 7 permutations]\Psi_0, where the permutations give the terms with different signs of components of vector k. The structure of \Psi_k is such that the excitation corresponds, in fact, to the replacement of \textbf{k}_l in some triple of sines from \Psi_0 by \textbf{k}. Such a structure of \Psi_0 and \Psi_k means that the crystal is created by sound: the ground state of a cubic crystal is formed by N identical three-dimensional standing waves similar to a longitudinal sound. It is also shown that the crystal in the ground state has a condensate of atoms with \textbf{k}=\textbf{k}_l. The nonclassical inertia moment observed in crystals He-4 can be related to the synchronous tunneling of condensate atoms.