The Kerr medium as an {\sf SU(2)} system

TL;DR

This paper applies Thermo Field Dynamics to exactly solve the Kerr medium with damping, revealing its SU(2) symmetry and expressing its dynamics as a Schrödinger-like equation, extended to multi-mode systems.

Contribution

It demonstrates the use of TFD techniques to solve the Kerr medium as an SU(2) spin system with damping, providing exact solutions and extending to multi-mode nonlinear oscillators.

Findings

Exact solution of the Kerr medium with damping using TFD.

Representation of system dynamics as a Schrödinger-like equation.

Extension of the method to multi-mode coupled nonlinear oscillators.

Abstract

The Kerr medium in the presence of damping and associated with SU(1,1) symmetry, is solved using the techniques of Thermo field Dynamics (TFD).These TFD techniques, well studied earlier (Chaturvedi and Srinivasan, 1991), help us to exactly solve the Kerr medium as a spin damped system associated with SU(2) symmetry. Using TFD, the association with SU(2) is exploited to express the dynamics of the system as a Schrodinger-like equation, whose solution is obtained using the appropriate disentanglement theorem. These considerations are extended to a system with multi-mode coupled nonlinear oscillators."