BC Toda chain I: reflection operator and eigenfunctions
N. Belousov, S. Derkachov, S. Khoroshkin
TL;DR
This paper derives integral representations for eigenfunctions of the BC-type quantum Toda chain with boundary interactions, introduces reflection and Baxter operators, and establishes their key properties.
Contribution
It introduces reflection operators satisfying reflection equations, constructs Baxter operators, and derives the Baxter equation for the BC Toda chain, advancing the understanding of boundary integrable systems.
Findings
Gauss-Givental integral representation for eigenfunctions
Reflection operators satisfying reflection equations
Baxter operators commuting with Hamiltonians and Baxter equation
Abstract
We obtain Gauss-Givental integral representation for the eigenfunctions of quantum Toda chain with boundary interaction of BC type. For this we introduce reflection operator satisfying reflection equation with DST chain Lax matrices. Besides, we define Baxter operators for BC Toda chain, prove their commutativity with Hamiltonians and derive the corresponding Baxter equation.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Quantum many-body systems · Nonlinear Waves and Solitons