https://doi.org/10.1140/epjp/i2017-11741-0
Regular Article
-symmetric rational Calogero model with balanced loss and gain
Department of Physics, Siksha-Bhavana, Visva-Bharati University, PIN 731 235, Santiniketan, India
* e-mail: debdeepsinha.rs@visva-bharati.ac.in
Received:
10
August
2017
Accepted:
3
October
2017
Published online:
7
November
2017
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 (
) and time reversal (
) 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 the exactly same ranges of the parameters for which the classical solutions are stable. The eigenspectrum 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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2017
