2012/01/11 by Maksim Tomchenko, M. D. Tomchenko, Tomchenko, M. D.
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Quantum, superfluid, helium dynamics #cond-mat.other
paper · pdf · doi:10.48550/arxiv.1201.2341
2 pages, submitted in Nature, v2: reference 8 is completed
openalex publication_date 2012/01/11 · arxiv created 2012/01/13 · arxiv updated 2012/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 kl=(π/Rx, π/Ry, π/Rz) (Rx, Ry, Rz 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.