Study of classical mechanical systems with complex potentials

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.

12 pages, 4 figures

References in corpus (4)

• Making Sense of Non-Hermitian Hamiltonians
• Factorizations of one dimensional classical systems
• Classical Trajectories for Complex Hamiltonians
• Complex Trajectories of a Simple Pendulum

Cited by in corpus (5)

• Time Fractional Schrödinger Equation; Fox's H-functions and the Effective Potential
• Various Scattering Properties of a New PT-symmetric non-Hermitian potential
• Approximate Dirac solutions of complex -symmetric Pöschl-Teller potential in view of spin and pseudospin symmetries
• Classical Trajectories of the Continuum States of the $\mathcal{P}\mathcal{T}$ symmetric Scarf II potential
• Effects of complex parameters on classical trajectories of Hamiltonian systems