# PT -symmetric rational Calogero model with balanced loss and gain

## TL;DR

This paper studies a PT-symmetric two-body rational Calogero model with balanced loss and gain, demonstrating its integrability, stability, and exact solutions in both classical and quantum regimes within specific parameter ranges.

## Contribution

It introduces a PT-symmetric Calogero model with balanced loss and gain, analyzing its classical and quantum stability, integrability, and exact solutions, which is a novel extension of traditional Calogero models.

## Key findings

- The system is integrable and admits exact classical solutions.
- Quantum bound states exist within specific parameter ranges.
- The eigen spectra and wave function normalization are discussed in detail.

## Abstract

A two body rational Calogero model with balanced loss and gain is investigated. The system yields a Hamiltonian which is symmetric under the combined operation of parity (P) and time reversal (T ) symmetry. It is shown that the system is integrable and exact, stable classical solutions are obtained for particular ranges of the parameters. The corresponding quantum system admits bound state solutions for exactly the same ranges of the parameters for which the classical solutions are stable. The eigen spectra of the system is presented with a discussion on the normalization of the wave functions in proper Stokes wedges. Finally, the Calogero model with balanced loss and gain is studied classically, when the pair-wise harmonic interaction term is replaced by a common confining harmonic potential. The system admits stable solutions for particular ranges of the parameters. However, the integrability and/or exact solvability of the system is obscure due to the presence of the loss and gain terms. The perturbative solutions are obtained and are compared with the numerical results.