Quantum dynamical localization

In the classical case, when the field intensity exceeds a threshold value, the electron s motion becomes chaotic and strong excitation and ionization takes place. In the quantum case instead, interference effects may lead to the suppression of the classical chaotic diffusion, the so-called quantum dynamical localization, and in order to ionize the atom, a larger field intensity is required (see Fig. 1). 

In conclusion, quantum dynamical localization plays an important role in the excitation and ionization process of atoms and molecules. A question that remains open in connection with the previous talk is whether quantization via periodic orbits can account for this phenomenon. 

From the last relationship the energetic symmetry displacement is noted, to the alpha branch, as an exponential fimction of the term which represents the effect of dynamic localization manifested by the standing waves this way, the quantum dynamic localization of the phases between the directions (on DS branches) is realized such that the photons pass from the field associated with the beta branch of the DS to the one associated with the alpha branch of DS, in order to keep the statistic equilibrium. 

Dennison coupling produces a pattern in the spectrum that is very distinctly different from the pattern of a pure nonnal modes Hamiltonian , without coupling, such as (Al.2,7 ). Then, when we look at the classical Hamiltonian corresponding to the Darling-Deimison quantum fitting Hamiltonian, we will subject it to the mathematical tool of bifiircation analysis [M]- From this, we will infer a dramatic birth in bifiircations of new natural motions of the molecule, i.e. local modes. This will be directly coimected with the distinctive quantum spectral pattern of the polyads. Some aspects of the pattern can be accounted for by the classical bifiircation analysis while others give evidence of intrinsically non-classical effects in the quantum dynamics. 

Minehardt T A, Adcock J D and Wyatt R E 1999 Quantum dynamics of overtone relaxation in 30-mode benzene a time-dependent local mode analysis for CH(v = 2) J. Chem. Phys. 110 3326-34... 

The obstacle to simultaneous quantum chemistry and quantum nuclear dynamics is apparent in Eqs. (2.16a)-(2.16c). At each time step, the propagation of the complex coefficients, Eq. (2.11), requires the calculation of diagonal and off-diagonal matrix elements of the Hamiltonian. These matrix elements are to be calculated for each pair of nuclear basis functions. In the case of ab initio quantum dynamics, the potential energy surfaces are known only locally, and therefore the calculation of these matrix elements (even for a single pair of basis functions) poses a numerical difficulty, and severe approximations have to be made. These approximations are discussed in detail in Section II.D. In the case of analytic PESs it is sometimes possible to evaluate these multidimensional integrals analytically. In either case (analytic or ab initio) the matrix elements of the nuclear kinetic energy... 

Let us now discuss the localizing effect of the POs described above. For this purpose we use the quantum dynamical method presented at the end of Section 3, with allow the construction of wave functions highly localized along the POs. In this sense, we refer to these functions as scar wave functions . 

At low temperatures (/3ho)c>l) the contributions from one-phonon, two-phonon processes, etc., can be systematically extracted from the general expression for the rate constant, and the type of the dominant process is determined by the bath spectrum and temperature. The results of Leggett et al. [1987] show that quantum dynamics of a TLS crucially depends on the spectrum of the bath. For sufficiently strong coupling, the bath may dramatically slow the tunneling rate, even to the point of localizing the particle in one of the wells. This strong dependence on the bath spectrum is inherent to the quantum dynamics and does not show up in classical transitions. 

In this section, we describe wave packet dynamics within a (time-dependent) local harmonic approximation to the potential, since this enables us to write down relatively simple expressions for the time evolution of the wave packet. This provides a valuable insight into quantum dynamics and the approximation may be used, for example, to... 

Recently, interesting symmetry effects have been discovered in connection with the quantum kicked rotor (see, e.g., Dittrich and Smilansky (1991a,b), Bliimel and Smilansky (1992), Thaha et al. (1993), Thaha and Bliimel (1994)). The issue concerns the influence of symmetries and their destruction on the localization length of the quantum kicked rotor. Can these symmetry effects be observed in atomic and molecular physics We think that this issue is important and propose the search for the influence of symmetry on the localization length of dynamically localizing systems as an interesting and important topic for future research. Therefore, the purpose of this section is to sketch briefly the essence of these recent discoveries as an incentive for their application in atomic and molecular physics. 

Jacobi and Schnepp (1972) and Raich (1972) were the first to develop a quantum-dynamical model for the large-amplitude librations in a-nitro-gen. Their formalism is essentially described in Section IV,C. They first calculated single-molecule mean field states that may be localized as well as delocalized, depending on the height of the rotation barriers from the anisotropic potential. These states were used to construct a basis of exci-tonlike wave functions for the whole crystal. The final step in their calcu-... 

Makarov, D. E., and Metiu, H., The reaction rate constant in a system with localized trajectories in the transition region Classical and quantum dynamics. 7. Chem. Phys. 107,... 

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