Classical oscillator with position-dependent mass in a complex domain

Abstract

We study complexified Harmonic Oscillator with a position-dependent mass, termed as Complex Exotic Oscillator (CEO). The complexification induces a gauge invariance [19,11]. The role of PT -symmetry is discussed from the perspective of classical trajectories of CEO for real energy. Some trajectories of CEO are similar to those for the particle in a quartic potential in the complex domain [10, 32].

20 pages, 4 figures, title is changed, some new features have been discussed, to appear in Phys. Lett. A

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• Chaotic systems in complex phase space
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• n-dimensional PDM non-linear oscillators: Linearizability and Euler-Lagrange or Newtonian invariance
• $n$-dimensional PDM-damped harmonic oscillators: Linearizability, and exact solvability