On time-dependent quasi-exactly solvable models

TL;DR

This paper explores the connection between quasi-exactly solvable quantum models and two classical dynamical systems, revealing new insights into their relationships and potential generalizations.

Contribution

It establishes a novel link between quantum solvable models and classical systems, including a generalization of the Calogero-Moser model and a classical matrix model.

Findings

Identifies a close relationship between quantum and classical models.

Proposes a generalization of the multi-particle Calogero-Moser model.

Connects quasi-exact solvability with classical matrix dynamics.

Abstract

In this paper we demonstrate that there exists a close relationship between quasi-exactly solvable quantum models and two special classes of classical dynamical systems. One of these systems can be considered a natural generalization of the multi-particle Calogero-Moser model and the second one is a classical matrix model.