The momentum distribution of two bosons in one dimension with infinite contact repulsion in harmonic trap gets analytical
Département de Physique. Laboratoire de physique quantique et systèmes dynamiques, Université Ferhat Abbas Sétif-1, 19000, Setif, Algeria
2 Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, 47011, Valladolid, Spain
3 UMR 7019, LPCT, Université de Lorraine-CNRS, 57000, Metz, France
Accepted: 13 June 2021
Published online: 6 July 2021
For a harmonically trapped system consisting of two bosons in one spatial dimension with infinite contact repulsion (hard core bosons), we derive an expression for the one-body density matrix in terms of center of mass and relative coordinates of the particles. The deviation from , the density matrix for the two fermions case, can be clearly identified. Moreover, the obtained allows us to derive a closed form expression of the corresponding momentum distribution . We show how the result deviates from the noninteracting fermionic case, the deviation being associated with the short-range character of the interaction. Mathematically, our analytical momentum distribution is expressed in terms of one and two variables confluent hypergeometric functions. Our formula satisfies the correct normalization and possesses the expected behavior at zero momentum. It also exhibits the high momentum tail with the appropriate Tan’s coefficient. Numerical results support our findings.
© The Author(s) 2021
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.