Chaotic systems in complex phase space

Abstract

This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviors of these two PT-symmetric dynamical models in complex phase space exhibit strong qualitative similarities.

22 page, 16 figures

References in corpus (13)

• The ODE/IM Correspondence
• PT-symmetric Deformations of the Korteweg-de Vries Equation
• Classical Trajectories for Complex Hamiltonians
• Complexified Dynamical Systems
• Quantum effects in classical systems having complex energy
• Spontaneous Breaking of Classical PT Symmetry
• Cryptogauge symmetry and cryptoghosts for crypto-Hermitian Hamiltonians
• Exceptional points in quantum and classical dynamics
• Exact Isospectral Pairs of PT-Symmetric Hamiltonians
• Classical oscillator with position-dependent mass in a complex domain
• Does the complex deformation of the Riemann equation exhibit shocks?
• Conduction bands in classical periodic potentials
• Quantum suppression of chaotic tunneling

Cited by in corpus (16)

• Complex Correspondence Principle
• Bohmian quantum trajectories from coherent states
• PT-symmetry breaking in complex nonlinear wave equations and their deformations
• Quantum tunneling as a classical anomaly
• Probability Density in the Complex Plane
• Understanding complex dynamics by means of an associated Riemann surface
• Conduction bands in classical periodic potentials
• Periodic orbits for classical particles having complex energy
• Classical Particle in a Complex Elliptic Potential
• Scaling laws of the out-of-time-order correlators at the transition to the spontaneous $\mathcal{P}\mathcal{T}$-symmetry breaking in a Floquet system
• Effective protection of quantum coherence by non-Hermitian driving
• Chaotic diffusion of complex trajectory and its quantum signature
• On regular and chaotic dynamics of a non-$\mathcal{P}\mathcal{T}$-symmetric Hamiltonian system of a coupled Duffing oscillator with balanced loss and gain
• PT-symmetrically deformed shock waves
• Quantum dynamics of PT-symmetrically kicked particle confined in a 1D box
• Effects of complex parameters on classical trajectories of Hamiltonian systems