Quartic anharmonic many-body oscillator

TL;DR

This paper introduces two quantum many-body models with quartic anharmonic interactions, extending well-known integrable systems, and analyzes them using algebraic perturbation theory and variational methods.

Contribution

It presents novel quartic anharmonic extensions of the Calogero and Wolfes models, maintaining their symmetries and providing new analytical approaches.

Findings

Models support the same symmetry as original systems

Algebraic perturbation theory applied successfully

Variational method used for analysis

Abstract

Two quantum quartic anharmonic many-body oscillators are introduced. One of them is the celebrated Calogero model (rational $A_n$ model) modified by quartic anharmonic two-body interactions which support the same symmetry as the Calogero model. Another model is the three-body Wolfes model (rational $G_2$ model) with quartic anharmonic interaction added which has the same symmetry as the Wolfes model. Both models are studied in the framework of algebraic perturbation theory and by the variational method.