Classical oscillator with position-dependent mass in a complex domain

TL;DR

This paper investigates a complexified harmonic oscillator with position-dependent mass, exploring its gauge invariance and PT-symmetry effects on classical trajectories, revealing similarities to quartic potential behaviors in the complex domain.

Contribution

It introduces the concept of a Complex Exotic Oscillator with position-dependent mass and analyzes its gauge invariance and PT-symmetry in the context of classical trajectories.

Findings

Complexification induces gauge invariance.

PT-symmetry influences classical trajectories.

Trajectories resemble those in quartic potentials.

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].