Driven coupled Morse oscillators --- visualizing the phase space and characterizing the transport

Abstract

Recent experimental and theoretical studies indicate that intramolecular energy redistribution (IVR) is nonstatistical on intermediate timescales even in fairly large molecules. Therefore, it is interesting to revisit the the old topic of IVR versus quantum control and one expects that a classical-quantum perspective is appropriate to gain valuable insights into the issue. However, understanding classical phase space transport in driven systems is a prerequisite for such a correspondence based approach and is a challenging task for systems with more then two degrees of freedom. In this work we undertake a detailed study of the classical dynamics of a minimal model system - two kinetically coupled coupled Morse oscillators in the presence of a monochromatic laser field. Using the technique of wavelet transforms a representation of the high dimensional phase space, the resonance network or Arnold web, is constructed and analysed. The key structures in phase space which regulate the dissociation dynamics are identified. Furthermore, we show that the web is nonuniform with the classical dynamics exhibiting extensive stickiness, resulting in anomalous transport. Our work also shows that pairwise irrational barriers might be crucial even in higher dimensional systems.

10 pages, 5 figures. Contribution to William H. Miller festschrift

References in corpus (10)

• Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum
• Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space
• Universality of algebraic laws in Hamiltonian systems
• Quantum-to-classical correspondence in open chaotic systems
• Intramolecular vibrational energy redistribution as state space diffusion: Classical-quantum correspondence
• Local phase space control and interplay of classical and quantum effects in dissociation of a driven Morse oscillator
• Overlapping resonances in the control of intramolecular vibrational redistribution
• Quantum Arnol'd Diffusion in a Simple Nonlinear System
• Bottlenecks to vibrational energy flow in OCS: Structures and mechanisms
• Reducing multiphoton ionization in a linearly polarized microwave field by local control

Cited by in corpus (10)

• Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective
• Visualization and comparison of classical structures and quantum states of 4D maps
• Dissociation dynamics of a diatomic molecule in an optical cavity
• Scaling perspective on Intramolecular vibrational energy flow: analogies, insights, and challenges
• What is the mechanism of power-law distributed Poincaré recurrences in higher-dimensional systems?
• Stable chaos and delayed onset of statisticality in unimolecular dissociation reactions
• Relevance of the resonance junctions on the Arnold web to dynamical tunneling and eigenstate delocalization
• Visualizing the Phase Space of the HeI_2 van der Waals Complex using Lagrangian Descriptors
• Power-law trapping in the volume-preserving Arnold-Beltrami-Childress map
• Stochastic modeling of spreading and dissipation in mixed-chaotic systems that are driven quasistatically