Eur. Phys. J. B (2014) 87: 207
https://doi.org/10.1140/epjb/e2014-41102-x

Regular Article

The Kerr medium as an SU(2) system: exact solution for spin damping

¹ Department of Theoretical Physics, University of Madras, Guindy Campus, 600025 Chennai, India
² Department of Physics, BITS Pilani, Hyderabad Campus, Jawahar Nagar, Shameerpet Mandal, 500078 Hyderabad, India
³ Indian Institute of Science Education and Research (IISER), Kolkata, 741246 Mohanpur, India

^a e-mail: pprasanta@iiserkol.ac.in

Received: 23 December 2013
Received in final form: 3 April 2014
Published online: 16 September 2014

Abstract

The non-linear Kerr medium in the presence of damping and earlier associated with an SU(1,1) symmetry, is exactly solved as a spin damped system, associated with an SU(2) symmetry. The association with SU(2) is exploited to express the dynamics of the system as a Schrödinger-like equation, whose solution is obtained using the appropriate disentanglement theorem. This method is then extended to multi-mode coupled nonlinear oscillators for obtaining exact solutions.