Mikito Toda

Bifurcation of no-return transition states in many-body chemical reactions

A new method is presented to study bifurcation of no-return transition states (TSs) at potential saddles for systems of many degrees of freedom (dof). The method enables us to investigate analytically when and how the no-return TS bifurcates. Our method reveals a new aspect of bifurcation for systems of many dof, i.e., the action variables of the bath dof play a role of control parameters as long as they remain approximately conserved. As an illustrative example, we demonstrate our new method by using a three atomic exchange reaction. The bifurcation of no-return TSs gives rise to a short-lived intermediate state at the saddle, which results in the overestimation of the reaction rate. Hence, the understanding of the bifurcation of the no-return TS is crucial to capture the complexity in kinetics and dynamics of the reactions. The definability of no-return TSs in many-body chemical reactions is also addressed under the occurrence of bifurcation above the reaction threshold.

Dynamical Hierarchy in Transition States of Reactions

Abstract.We present a partial normalization procedure of Lie canonical perturbation theory to elucidate the phase space geometry of the transition state in the multidimensional phase space for a wide range of energy above the threshold. State selectivity and dynamical correlation along the evolution of reactions will also be discussed.

Phase retrieval problem in quantum chaos and its relation to the origin of irreversibility I

Abstract The purpose of this paper are (i) to study characteristics features of phase in quantum dynamics corresponding to chaos, and (ii) to discuss implication of these features for the origin of irreversibility. The first is done by focusing attention on topological defects of phase in the Husimi representation. We find that the process of generating topological defects corresponds to the folding of Morse-Smale horseshoe dynamics. Moreover, the distribution of topological defects changes from regular to random under the time evolution. This change is a distinctive feature of quantum dynamics corresponding to chaos. The second is done in terms of phase retrieval problem. We present numerical results which strongly suggest the following. The randomness in the distribution of topological defects is the cause of difficulty in retrieving phase. Based on these results we present the following hypothesis. The loss of phase information in statistical mechanics can be understood in terms of the randomness of phase in quantum dynamics corresponding to chaos.

Breakdown mechanisms of normally hyperbolic invariant manifolds in terms of unstable periodic orbits and homoclinic/heteroclinic orbits in Hamiltonian systems

We analyze the mechanism of breakdown of normally hyperbolic invariant manifolds (NHIMs) based on unstable periodic orbits, homoclinic and heteroclinic orbits in NHIMs for Hamiltonian systems. First, we classify the breakdown mechanism in terms of the characteristic multipliers (the eigenvalues of the phase space Jacobian matrix) of unstable periodic orbits in the NHIM and elucidate the classification for systems of three degrees of freedom. Second, we also present an index that provides a sufficient condition under which the NHIM ceases to exist in more global regions along the homoclinic and heteroclinic orbits in the NHIM. We demonstrate local and global features of the breakdown of the NHIM for a hydrogen atom in crossed electric and magnetic fields. Our analysis of unstable periodic orbits of shorter periods indicates that local features of the breakdown are highly inhomogeneous, depending on each periodic orbit. This manifests an inherent dynamical feature for systems of more than two degrees of freedom. Contrastingly, our analysis of homoclinic orbits indicates that the energy at which the NHIM breaks down does not depend on each homoclinic orbit. This result suggests the existence of a global breakdown of the NHIM behind these homoclinic orbits since these homoclinic orbits run through broader phase space regions.

Nonexponential decays resulting from crises in predissociation of a highly excited van der Waals complex

Abstract Scattering in a highly excited van der Waals complex HeI2 is investigated in quantum mechanics. Particular attention is paid to crisis, where homoclinic tangency of the stable and unstable manifolds leads to a transition in chaos. Crisis in classical chaos gives rise, in the corresponding quantum system, to multiple decay paths with distinct decay times. The resulting effects are nonexponential decays in the predissociation processes and a transition in the distribution of final rotational states. Implications of these results for control of reaction processes are briefly discussed.

Quantal version of resonance overlap

A quantal version of resonance overlap leading to global chaos is investigated. Classical chaos is reflected in irregular features of quantum beats in the phase space profile of eigenfunctions. These quantum beats are due to interference between nearby branches of bifurcated classical manifolds. Statistical properties of the quantum system qualitatively reflect the classical transition to global chaos although some discrepancies from classical ergodicity are found in the quantum mechanics even in the fully chaotic regime.

Wavelet Analysis and Arnold Web Picture for Detecting Energy Transfer in a Hamiltonian Dynamical System

Our motivation is to understand how, in chemical reactions, the reaction coordinate effectively gains dynamical energy from the other degrees of freedom (i.e., bath coordinates) avoiding thermalization of the redistributed energy. In such a system, the phase space structure should be not homogeneous; i.e., the system is never ergodic. In this study, we introduce a way to capture the inhomogeneity of the phase space and to monitor energy transfers among their partial degrees of freedom in nonergodic systems using wavelet analysis and a picture of the Arnold web. First, we examine several simple energy transfer processes, i.e., a motion on a resonance line, between resonance lines, and around a resonance junction in a simple three-degree-of-freedom (DOF) system and show how the elemental processes of the intramolecular vibrational energy redistribution (IVR) are detected by our tools. We especially note that the structure of the higher order resonance of the system can be detected by wavelet analysis and motion in the action space. Next, we analyze a reaction process in a simple Hamiltonian system of 3 DOF with a double-well potential, i.e., a system with a transition state of the center-saddle-center type, and detect energy transfers in the reactive process. The aim of the study is to propose a way to characterize the inhomogeneity of the phase space, e.g., the reactive doorway, which leads to controllability of the chemical reaction by light, i.e., control of the reaction by selectively preparing an initial state in the reactive doorway by optical excitation.

Spatio-temporal hierarchy in the dynamics of a minimalist protein model.

A method for time series analysis of molecular dynamics simulation of a protein is presented. In this approach, wavelet analysis and principal component analysis are combined to decompose the spatio-temporal protein dynamics into contributions from a hierarchy of different time and space scales. Unlike the conventional Fourier-based approaches, the time-localized wavelet basis captures the vibrational energy transfers among the collective motions of proteins. As an illustrative vehicle, we have applied our method to a coarse-grained minimalist protein model. During the folding and unfolding transitions of the protein, vibrational energy transfers between the fast and slow time scales were observed among the large-amplitude collective coordinates while the other small-amplitude motions are regarded as thermal noise. Analysis employing a Gaussian-based measure revealed that the time scales of the energy redistribution in the subspace spanned by such large-amplitude collective coordinates are slow compared to the other small-amplitude coordinates. Future prospects of the method are discussed in detail.

Absorption of light by a quantum chaos system

Abstract A simple quantum chaos system is examined as a model with which a realistic process of light absorption can be simulated. A typical quantum chaos system composed of two degrees of freedom does not absorb light stationarily, that is, at a constant rate. However, when it is coupled with only one or two other degrees of freedom, the results of simulation strongly suggest that the chaotic system absorbs light stationarily even though the coupling strength is quite weak. This fact provides a direct evidence that quantum chaos may be an origin of dissipation in quantum systems with a few degrees of freedom.

Recovery of Liouville dynamics in quantum mechanical suppressed chaotic behavior

It is shown that classical Liouville dynamics are recovered from quantum mechanically suppressed chaotic motion by introducing a measurement process into the pure dynamics. Such a process is a quantum non-demolition measurement for information on the phase space probability distribution. A fully quantum dynamical model of such a process, which is based on a von Neumanns (1932) lattice basis, is proposed. The quantum fluctuations of the measurement system releases the host system from a quantum suppression, thereby restoring an entire classical motion in the phase space.