Quantum-Chaotic Evolution Reproduced from Effective Integrable Trajectories

Abstract

Classically integrable approximants are here constructed for a family of predominantly chaotic periodic systems by means of the Baker-Hausdorff-Campbell formula. We compare the evolving wave density for the corresponding exact quantum systems using semiclassical approximations based alternatively on the chaotic and on the integrable trajectories. It is found that the latter reproduce the quantum oscillations and provide superior approximations even when the initial coherent state is placed in a broad chaotic region. Time regimes are then accessed in which the propagation based on the system's exact chaotic trajectories breaks down.

arXiv comment5 pages, 3 figures

References in corpus (7)

• Resonance-assisted tunneling in near-integrable systems
• Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime
• The Importance of the Pre-exponential Factor in Semiclassical Molecular Dynamics
• How do wave packets spread? Time evolution on Ehrenfest time scales
• Quantum revival patterns from classical phase-space trajectories
• A Classification Framework for Partially Observed Dynamical Systems
• Semiclassical evolution in phase space for a softly chaotic system

Cited by in corpus (3)

• Complexified phase spaces, initial value representations, and the accuracy of semiclassical propagation
• Are quantum trajectories suitable for semiclassical approximations?
• Harmonic oscillator kicked by spin measurements: a Floquet-like system without classical analogous