Discontinuity, Nonlinearity, and Complexity
Integrability of a Coupled Harmonic Oscillator in Extended Complex Phase Space
Discontinuity, Nonlinearity, and Complexity 4(1) (2015) 3548  DOI:10.5890/DNC.2015.03.004
Ram Mehar Singh
Department of Physics, Ch. Devi Lal University, Sirsa125055, Haryana, India
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Abstract
With in the frame work of extended complex phase space characterized by x = x1 + ip3, y = x2 + ip4, px = p1 + ix3 and py = p2 + ix4, we investigate the exact invariants for a coupled harmonic oscillator along with PTsymmetric version in two dimensions. For this purpose rationalization method is employed and the invariants obtained in this work play an important role to study the complex trajectories of the concerned classical system.
Acknowledgments
The author expresses his gratitude to Prof. S.C. Mishra and Dr. Fakir Chand, Department of Physics, Kurukshetra University, Kurukshetra (India), for their valuable suggestions regarding the manuscript. He is also thankful to the referees for their useful comments which helped in finetuning of some basic ideas in original version of the paper.
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