Study of classical mechanical systems with complex potentials

TL;DR

This paper explores classical mechanical systems with complex potentials, using factorization techniques to analyze PT symmetric models, revealing how classical trajectories change from closed to open as symmetry breaks.

Contribution

It applies a factorization method to classical systems with complex potentials, specifically analyzing PT symmetric models and their symmetry-breaking phenomena.

Findings

Classical trajectories transition from closed to open at PT symmetry breaking point.

The factorization technique effectively analyzes complex classical systems.

PT symmetric models exhibit distinct classical behavior at critical parameters.

Abstract

We apply the factorization technique developed by Kuru and Negro [Ann. Phys. 323 (2008) 413] to study complex classical systems. As an illustration we apply the technique to study the classical analogue of the exactly solvable PT symmetric Scarf II model, which exhibits the interesting phenomenon of spontaneous breakdown of PT symmetry at some critical point. As the parameters are tuned such that energy switches from real to complex conjugate pairs, the corresponding classical trajectories display a distinct characteristic feature - the closed orbits become open ones.