2021/08/08 by Maksim Tomchenko, Tomchenko, Maksim D.
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Quantum Mechanics and Applications #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2108.03633
openalex publication_date 2021/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.