Spectral analysis of an open $q$-difference Toda chain with two-sided boundary interactions on the finite integer lattice

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: van Diejen, Jan Felipe
Format: Preprint
Published: 2023
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866909117253156864
author van Diejen, Jan Felipe
author_facet van Diejen, Jan Felipe
contents A quantum $n$-particle model consisting of an open $q$-difference Toda chain with two-sided boundary interactions is placed on a finite integer lattice. The spectrum and eigenbasis are computed by establishing the equivalence with a previously studied $q$-boson model from which the quantum integrability is inherited. Specifically, the $q$-boson-Toda correspondence in question yields Bethe Ansatz eigenfunctions in terms of hyperoctahedral Hall-Littlewood polynomials and provides the pertinent solutions of the Bethe Ansatz equations via the global minima of corresponding Yang-Yang type Morse functions.
format Preprint
id arxiv_https___arxiv_org_abs_2304_05466
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Spectral analysis of an open $q$-difference Toda chain with two-sided boundary interactions on the finite integer lattice
van Diejen, Jan Felipe
Mathematical Physics
Exactly Solvable and Integrable Systems
Primary: 33D52, Secondary: 05E05, 81Q35, 81Q80, 81U15, 82B23
A quantum $n$-particle model consisting of an open $q$-difference Toda chain with two-sided boundary interactions is placed on a finite integer lattice. The spectrum and eigenbasis are computed by establishing the equivalence with a previously studied $q$-boson model from which the quantum integrability is inherited. Specifically, the $q$-boson-Toda correspondence in question yields Bethe Ansatz eigenfunctions in terms of hyperoctahedral Hall-Littlewood polynomials and provides the pertinent solutions of the Bethe Ansatz equations via the global minima of corresponding Yang-Yang type Morse functions.
title Spectral analysis of an open $q$-difference Toda chain with two-sided boundary interactions on the finite integer lattice
topic Mathematical Physics
Exactly Solvable and Integrable Systems
Primary: 33D52, Secondary: 05E05, 81Q35, 81Q80, 81U15, 82B23
url https://arxiv.org/abs/2304.05466