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Volume 18, Issue 3, September 2011, Pages 475 - 482
2D Locus Configurations and the Trigonometric Calogero–Moser System
Authors
Greg Muller
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70808, USA,gmuller@lsu.edu
Received 23 February 2011, Accepted 18 May 2011, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925111001726How to use a DOI?
- Keywords
- Schrödinger operator; locus configuration; Baker–Akhiezer function; Calogero–Moser equation; particle systems
- Abstract
A central hyperplane arrangement in ℂ2 with multiplicity is called a “locus configuration” if it satisfies a series of “locus equations” on each hyperplane. Following [4], we demonstrate that the first locus equation for each hyperplane corresponds to a force-balancing equation on a related interacting particle system on ℂ*: the charged trigonometric Calogero-Moser system. When the particles lie on S1 ⊂ ℂ*, there is a unique equilibrium for this system. For certain classes of particle weight, this is enough to show that all the locus equations are satisfied, producing explicit examples of real locus configurations. This in turn produces new examples of Schrödinger operators with Baker–Akhiezer functions.
- Copyright
- © 2011 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
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Cite this article
TY - JOUR AU - Greg Muller PY - 2021 DA - 2021/01/07 TI - 2D Locus Configurations and the Trigonometric Calogero–Moser System JO - Journal of Nonlinear Mathematical Physics SP - 475 EP - 482 VL - 18 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925111001726 DO - 10.1142/S1402925111001726 ID - Muller2021 ER -