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Complex dynamical invariant for a PT- symmetric Hamiltonian system in higher dimensions

Authors:	S.B. Bhardwaj Ram Mehar Singh Kushal Sharma

Affiliation:	1. Department of Applied Sciences, Chandigarh Engineering College, Landran, Mohali-140307, India;2. Department of Physics, Chaudhary Devi Lal University, Sirsa-125055, India;3. Department of Mathematics, National Institute of Technology, Hamirpur-177005, India

Abstract:	With a view to get further insight into the integrability of a dynamical system, we investigate the complex invariant for a three-dimensional Hamiltonian system using the extended complex phase space approach (ECPSA) characterized by $x = x_{1} + i p_{4}, y = x_{2} + i p_{5}, z = x_{3} + i p_{6}, p_{x} = p_{1} + i x_{4}, p_{y} = p_{2} + i x_{5}$ and $p_{z} = p_{3} + i x_{6}$ . For this purpose the rationalization method is utilized and the invariant obtained is expected to play an important role in the study of the complex trajectories for the system of concern.

Keywords:	Integrability Complex invariants Non-hermitian Hamiltonian Rationalization method
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