A class of complex solutions to the time-independent Hamilton-Jacobi equation in the real-valued configuration space that represent multidimensional nonclassical motions such as dynamical tunneling, namely, energetically allowed but dynamically forbidden transition, as well as the ordinary tunneling are shown. We introduce a quantity called ``parity of motion'' into each coordinate in configuration space for the Hamilton-Jacobi equation and thereby construct the solutions. Positive parity induces merely ordinary classical motion, while negative parity allows nonclassical motion such as tunneling. These solutions are classified by a given set of parities, each class of which forms a sheet in the entire solution space. New canonical equations of motion are derived with which nonclassical paths are generated in each sheet. Furthermore, it is shown that each sheet is associated with two kinds of action integrals: One, which is real valued, satisfies the principle of least action, thereby generating both ordinary and tunneling trajectories, but is not a solution to the Hamilton-Jacobi equation, while the other action is a solution to the time-independent Hamilton-Jacobi equation, and is complex valued in a tunneling region. Only in Newtonian mechanics, which forms an extreme sheet having all the parities positive, do these two actions happen to coincide with each other. Numerical examples for dynamical tunneling among tori in the H\'enon-Heiles system and ordinary potential tunneling in a three-dimensional system are presented.
We reexmine the mechanism and interpretation of photochemical reaction of phenol molecule with small ammonia clusters, which is schematically written as Ph*OH···(NH(3))(n) → PhO(•)···[H(NH(3))(n)]*(•) with n ≤ 5. The low-lying excited states of this system in the adiabatic representation are densely quasi-degenerate due to the presence of the Rydberg-like diffused states in ammonia clusters. To treat the dynamics on such highly quasi-degenerate electronic states, we have carried out a large scale semiclassical Ehrenfest dynamics, nonadiabatic electron wavepacket dynamics in terms of very many configuration-state functions, to track the nonadiabatic electron and proton transfer dynamics in the time step of attosecond scale, integrating up to 300 fs. It turns out that the mechanism is more complicated than that referred to as excited-state hydrogen-atom transfer, which is widely accepted now. The pathways of jumping electron and shifting proton nucleus are identified to be mutually different, which necessarily results in charge separation in ammonia clusters after the transitions. The global feature of the present transfer dynamics is fully analyzed as one of the general prototypes of coupled electron-proton transfer in excited states.
We study the dynamics of spatiotemporal pattern formation in a nonlinear proliferation system (e.g., cell division supported on a field of nutrition), in which the mechanism of activation and its self-suppression is simultaneously implemented. This dynamical model has been numerically realized with coupled cellular automata (CA), and various long-standing spatiotemporal patterns have been observed. Among others, a successive generation of traveling waves by implanting a spot of cells onto the field consisting of nutrition and activator is particularly interesting. This takes place despite the fact that the present reaction network has a stable fixed point and therefore autonomous temporal oscillatory does not exist in the mean field. Indeed, the reaction-diffusion equation method (RD) applied to this network reproduces only a single excitable wave and soon falls into a steady state (a fixed point) without the following propagating waves. This system, having a stable fixed point, is an excitable system of different kind from the FitzHugh-Nagumo model in that it can generate a pulse propagating outwards by adding only a single cell onto it from outside the system. The present excitation upon dropping a cell is amplified to macroscopic level by a hidden dynamics of oscillation between the activation and its self-suppression. A pulse thus generated is propagated in space time with the help of diffusion. Through a precise comparison between CA and RD, it is found that a very small amount of residue of the cells and activators, which are left unburned in the stochastic treatment of reactions by the CA, becomes a seed to excite the system and generate the next pulse wave. This newly born wave can leave another seed of reaction in the field after its propagation. Based on this analysis, we account for the appearance of other patterns observed. A possible control of these patterns by varying the spatial distribution of initial concentration of the relevant agents such as the activator is also discussed.
We propose a new formulation for a photodissociation process to which an expansional (or algebraic) quantum-variation-method of scattering is applicable. By solving a ’’full collision’’ problem which describes a multichannel process on the repulsive surface, the photodissociation scheme takes account of interchannel coupling from the outset. Our expression for the amplitude of the partial linewidth is similar to that of the ’’half-collision’’ approximation of Jortner et al. The present formalism differs in that the scattering wave functions take acount of interchannel coupling exactly. As a result, only on-the-energy-shell contributions appear in the partial linewidth.
Gekoppelte Rotation: Theoretische Untersuchungen zur Dynamik des Protonentransfers in 5-Methyltropolon (5MTR) enthüllen eine langreichweitige mechanische Wechselwirkung: Der Protonentransfer treibt die Rotation einer Methylgruppe an, da Hyperkonjugation und Tautomerisierung in 5MTR gekoppelt sind (siehe HOMO-LUMO-Wechselwirkung). Ein quantenmechanischer Mechanismus wird vorgestellt, dem zufolge ein Konformationswechsel im Molekül stattfindet.
The validity range of the Born-Oppenheimer (BO) approximation is studied with respect to the variation of the mass (m) of negatively charged particle by substituting an electron (e) with muon (mu) and antiproton (p) in hydrogen molecule cation. With the use of semiclassical quantization applied to these (ppe), (ppmu), and (ppp) under a constrained geometry, we estimate the energy difference of the non-BO vibronic ground state from the BO counterpart. It is found that the error in the BO approximation scales to the power of 3/2 to the mass of negative particles, that is, m(1.5). The origin of this clear-cut relation is analyzed based on the original perturbation theory due to Born and Oppenheimer, with which we show that the fifth order term proportional to m(5/4) is zero and thereby the first correction to the BO approximation should arise from the sixth order term that is proportional to m(6/4). Therefore, the validity range of the Born-Oppenheimer approximation is wider than that often mistakenly claimed to be proportional to m(1/4).
An iterative approach to the solution of the Lippmann-Schwinger integral equation for electron-molecule scattering, based on the use of the Schwinger variational principle is outlined. Application of the theory to electron-molecule collisions at the static-exchange level and for use with optical potentials, and a new variational principle for the strong polar molecule case, are discussed. Results of some applications of these methods to a few systems are considered and some results of the use of the method for molecular photoionization are presented. Multichannel extensions of the Schwinger variational principle are discussed and some results as applied to a simple and exactly soluble two-channel model problem presented.
