On the probable wave nature of Bose crystals

TL;DR

This paper presents exact wave function solutions for Bose crystals, proposing that their structure is formed by standing sound waves and suggesting a wave-based origin for crystalline order, with implications for superfluidity in solid helium.

Contribution

It provides the first exact solutions for Bose crystal wave functions under natural boundary conditions, revealing a wave-based mechanism for crystal formation.

Findings

Crystals are formed by standing waves in the probability field.

Ground state contains a condensate with a specific wave vector.

Lattice periodicity is caused by sound waves, not just energy minimization.

Abstract

At the present time, it is considered that Bose crystals are formed at the cooling of a fluid, because the state of crystal is more favorable by energy. It is also believed [1,2] that no ordering factor forming a crystal is present, except for the interatomic interaction. However, the available solutions [1,2,3] for the wave functions (WFs) of the ground and excited states of a crystal are approximate and are obtained for cyclic boundary conditions, which are not realized in the Nature. Here, we present the exact solutions for the WFs of a Bose crystal with rectangular lattice under natural zero boundary conditions. The structure of WFs implies that 1) a crystal is formed by a standing wave in the probability field; 2) a crystal in the ground state contains a condensate of atoms with the wave vector \textbf{k}_l=(\pi/\bar{R}_x, \pi/\bar{R}_y, \pi/\bar{R}_z) (\bar{R}_x, \bar{R}_y, \bar{R}_z are the periods of the lattice) that is equal to a half of the vector of the reciprocal lattice. These solutions indicate that the ordering factor forming a crystal is an intense standing wave similar to a sound one. Thus, the periodicity of a lattice is caused by that of a sound wave, but not only by the energy minimum principle. Apparently, the crystals of other types and with different lattices have the wave nature as well. The condensate opens a possibility to explain the nonclassical inertia moment discovered by Kim and Chan [4,5] in solid He-4, which testifies, probably, to the presence of a superfluid subsystem in the crystal.