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Title: Exact solutions of two complementary one-dimensional quantum many-body systems on the half-line

Abstract

We consider two particular one-dimensional quantum many-body systems with local interactions related to the root system C{sub N}. Both models describe identical particles moving on the half-line with nontrivial boundary conditions at the origin, but in the first model the particles interact with the delta interaction while in the second via a particular momentum dependent interaction commonly known as delta-prime interaction. We show that the Bethe ansatz solution of the delta-interaction model is consistent even for the general case where the particles are distinguishable, whereas for the delta-prime interaction it only is consistent and nontrivial in the fermion case. We also establish a duality between the bosonic delta- and the fermionic delta-prime model, and we elaborate on the physical interpretations of these models.

Authors:
;  [1]
  1. Mathematical Physics, KTH Physics, AlbaNova, SE-106 91 Stockholm (Sweden)
Publication Date:
OSTI Identifier:
20699161
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 46; Journal Issue: 5; Other Information: DOI: 10.1063/1.1865320; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSONS; BOUNDARY CONDITIONS; DUALITY; EIGENVALUES; EXACT SOLUTIONS; FERMIONS; MANY-BODY PROBLEM; ONE-DIMENSIONAL CALCULATIONS; QUANTUM MECHANICS

Citation Formats

Hallnaes, Martin, and Langmann, Edwin. Exact solutions of two complementary one-dimensional quantum many-body systems on the half-line. United States: N. p., 2005. Web. doi:10.1063/1.1865320.
Hallnaes, Martin, & Langmann, Edwin. Exact solutions of two complementary one-dimensional quantum many-body systems on the half-line. United States. https://doi.org/10.1063/1.1865320
Hallnaes, Martin, and Langmann, Edwin. 2005. "Exact solutions of two complementary one-dimensional quantum many-body systems on the half-line". United States. https://doi.org/10.1063/1.1865320.
@article{osti_20699161,
title = {Exact solutions of two complementary one-dimensional quantum many-body systems on the half-line},
author = {Hallnaes, Martin and Langmann, Edwin},
abstractNote = {We consider two particular one-dimensional quantum many-body systems with local interactions related to the root system C{sub N}. Both models describe identical particles moving on the half-line with nontrivial boundary conditions at the origin, but in the first model the particles interact with the delta interaction while in the second via a particular momentum dependent interaction commonly known as delta-prime interaction. We show that the Bethe ansatz solution of the delta-interaction model is consistent even for the general case where the particles are distinguishable, whereas for the delta-prime interaction it only is consistent and nontrivial in the fermion case. We also establish a duality between the bosonic delta- and the fermionic delta-prime model, and we elaborate on the physical interpretations of these models.},
doi = {10.1063/1.1865320},
url = {https://www.osti.gov/biblio/20699161}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 5,
volume = 46,
place = {United States},
year = {Sun May 01 00:00:00 EDT 2005},
month = {Sun May 01 00:00:00 EDT 2005}
}