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 classicalquantum 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.

Visualization and comparison of classical structures and quantum states of four-dimensional maps

“…We now compare the 3d phase-space slices with the frequency analysis [52][53][54][55]. This method associates each regular torus with its two fundamental frequencies (ν 1 , ν 2 ) ∈ [0, 1[ 2 , which are displayed in the 2d frequency plane, see Fig.…”

“…Starting with the pioneering work of Froeschlé [43,44] several methods have been introduced to obtain a reduction to understand the dynamics. For example two-dimensional plots of multi-sections [44,45] or projections to two [2,43,46] or three [47][48][49] dimensions, also including color to indicate the projected coordinate [50,51], frequency analy- sis [52][53][54][55], and action-space plots [56] . Further tools to investigate higher-dimensional phase spaces are chaos indicators to distinguish regular from chaotic motion, like finite-time Lyapunov exponents [57][58][59], Fast Lyapunov Indicator [45,60,61], and many more, see e.g.…”

Stable chaos and delayed onset of statisticality in unimolecular dissociation reactions

“…However, the extent to which quantum effects like dynamical tunnelling [65,66] can lead to enhanced localisation or de-trapping from the junctions [44,67] requires a systematic study of the classical and quantum dynamics near the junctions, particularly those with multiplicities greater than two. Such studies, given the modest effective dimensionality of the vibrational state space even for large molecules [68], may prove important towards the possibility of control by nudging the system to the regions of stable chaos using weak external fields [69][70][71]. Fig.…”

Scaling Perspective on Intramolecular Vibrational Energy Flow: Analogies, Insights, and Challenges

“…An example for sticky behavior and importance of pairwise noble barriers in higher DoFs comes from a recent study [176] of driven, coupled Morse oscillators. The Hamiltonian is given by…”