dorsal/arxiv
View SchemaPotential Harmonics Expansion Method for Trapped Interacting Bosons : Inclusion of Two-Body Correlation
| Authors | T. K. Das, B. Chakrabarti |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0408061 |
| URL | https://arxiv.org/abs/quant-ph/0408061 |
| DOI | 10.1103/PhysRevA.70.063601 |
Abstract
We study a system of $A$ identical interacting bosons trapped by an external field by solving ab initio the many-body Schroedinger equation. A complete solution by using, for example, the traditional hyperspherical harmonics (HH) basis develops serious problems due to the large degeneracy of HH basis, symmetrization of the wave function, calculation of the matrix elements, etc. for large $A$. Instead of the HH basis, here we use the "potential harmonics" (PH) basis, which is a subset of HH basis. We assume that the contribution to the orbital and grand orbital [in $3(A-1)$-dimensional space of the reduced motion] quantum numbers comes only from the interacting pair. This implies inclusion of two-body correlations only and disregard of all higher-body correlations. Such an assumption is ideally suited for the Bose-Einstein condensate (BEC), which is extremely dilute. Unlike the $(3A-4)$ hyperspherical variables in HH basis, the PH basis involves only three {\it{active}} variables. It drastically reduces the number of coupled equations and calculation of the potential matrix becomes tremendously simplified, as it involves integrals over only three variables for any $A$. One can easily incorporate realistic atom-atom interactions in a straight forward manner. We study the ground and excited state properties of the condensate for both attractive and repulsive interactions for various particle number.
{
"annotation_id": "c14d7372-ed68-4272-8356-ad0cddf49fb9",
"date_created": "2026-03-02T18:02:10.393000Z",
"date_modified": "2026-03-02T18:02:10.393000Z",
"file_hash": "601c857932df0ca2f52e69cfcc3c70780b2d83b877c1e13b22d52df060a28718",
"private": false,
"record": {
"abstract": "We study a system of $A$ identical interacting bosons trapped by an external\nfield by solving ab initio the many-body Schroedinger equation. A complete\nsolution by using, for example, the traditional hyperspherical harmonics (HH)\nbasis develops serious problems due to the large degeneracy of HH basis,\nsymmetrization of the wave function, calculation of the matrix elements, etc.\nfor large $A$. Instead of the HH basis, here we use the \"potential harmonics\"\n(PH) basis, which is a subset of HH basis. We assume that the contribution to\nthe orbital and grand orbital [in $3(A-1)$-dimensional space of the reduced\nmotion] quantum numbers comes only from the interacting pair. This implies\ninclusion of two-body correlations only and disregard of all higher-body\ncorrelations. Such an assumption is ideally suited for the Bose-Einstein\ncondensate (BEC), which is extremely dilute. Unlike the $(3A-4)$ hyperspherical\nvariables in HH basis, the PH basis involves only three {\\it{active}}\nvariables. It drastically reduces the number of coupled equations and\ncalculation of the potential matrix becomes tremendously simplified, as it\ninvolves integrals over only three variables for any $A$. One can easily\nincorporate realistic atom-atom interactions in a straight forward manner. We\nstudy the ground and excited state properties of the condensate for both\nattractive and repulsive interactions for various particle number.",
"arxiv_id": "quant-ph/0408061",
"authors": [
"T. K. Das",
"B. Chakrabarti"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.70.063601",
"title": "Potential Harmonics Expansion Method for Trapped Interacting Bosons : Inclusion of Two-Body Correlation",
"url": "https://arxiv.org/abs/quant-ph/0408061"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "953aa6e4-5350-42f0-813d-3730b554f471",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}