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  • 1
    Digitale Medien
    Digitale Medien
    Avoided crossings, scars, and transition to chaos (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 2395-2406 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: The correlation diagram of the LiNC/LiCN isomerizing system as a function of (h-dash-bar), taken as a parameter, is considered in conditions of widespread classical chaos. Two series of isolated avoided crossings of very different nature, involving states related by the same 1:8 quantum resonance condition, are characterized and the corresponding interaction matrix elements between adiabatic states analytically calculated and analyzed. One of these series has been found to separate two distinct regions: one for smaller values of (h-dash-bar) (at any given energy) corresponding to regular states, i.e., with a definite nodal pattern, and the other of much more stochastic behavior. Moreover, the effect of the interaction involved in these avoided crossings is to mix the regular wave functions giving rise to wave functions strongly scarred by the periodic orbits of the associated 1:8 classical resonance. This result constitutes an interpretation of the scarring effect from a new perspective. © 1997 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.474582
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  • 2
    Digitale Medien
    Digitale Medien
    Semiclassical quantization of fragmented tori: Application to saddle-node states of LiNC/LiCN (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 7934-7942 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: A new implementation of the EBK method for the semiclassical quantization of partially destroyed tori is presented. The application to the calculation of some quantum states of the LiNC/LiCN molecule which are influenced by a saddle-node bifurcation is discussed. In this quantization surrogates of invariant tori, computed using gap filling saddle-node orbits, are used. These orbits are obtained from a very detailed study of the islands around islands structure existing in the relevant classical phase space region. © 1997 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.475147
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  • 3
    Digitale Medien
    Digitale Medien
    A periodic orbit analysis of the vibrationally highly excited LiNC/LiCN: A comparison with quantum mechanics (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 2921-2931 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: By constructing continuation/bifurcation diagrams of families of periodic orbits of LiNC/LiCN system the spectroscopy and dynamics for this species are deduced and compared with accurate quantum mechanical calculations up to 13 000 cm−1. The interesting phenomenon of the appearance of gaps in the continuation diagram of the principal family that corresponds to the bend motion is shown to occur in both isomers, LiNC and LiCN. Through semiclassical quantization a one to one correspondence of specific periodic orbits to certain eigenstates is demonstrated. One interesting example is the case of periodic orbits that are generated from a saddle-node bifurcation and describe rotations of the Li+ ion around the CN− fragment. The correspondence of these periodic orbits to regular rotating type eigenfunctions is shown, thus, demonstrating in a clear way the importance of the saddle-node bifurcations in locating localized wavefunctions in highly energized molecules. © 1996 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.471113
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  • 4
    Digitale Medien
    Digitale Medien
    Transition from order to chaos in molecular wave functions and spectra (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 6401-6404 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: In this Communication we describe how the transition from regularity to classical chaos in molecular Hamiltonian systems shows up at the quantum level in the structure of the corresponding wave functions and spectra. By changing the value of (h-dash-bar) we show how the scars result from combinations of regular wave functions. © 1996 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.471301
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  • 5
    Digitale Medien
    Digitale Medien
    Saddle-node bifurcations in the LiNC/LiCN molecular system: Classical aspects and quantum manifestations (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 5068-5081 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: A classical-quantum correspondence study of a saddle-node bifurcation in a realistic molecular system is presented. The relevant classical structures (periodic orbits and manifolds) and its origin are examined in detail. The most important conclusion of this study is that, below the bifurcation point, there exists an infinite sequence of precursor orbits, which mimic for a significant period of time the (future) saddle-node orbits. These structures have a profound influence in the quantum mechanics of the molecule and several vibrational wave functions of the system present a strong localization along the saddle-node periodic orbits. A striking result is that this scarring effect also takes place well below the bifurcation energy, which constitutes a manifestation of the so-called "ghost'' orbits in configuration and phase space. This localization effect has been further investigated using wave packet dynamics. © 1996 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.472351
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  • 6
    Digitale Medien
    Digitale Medien
    Adiabatic energies and radial couplings of the 3Σ+u states of H2 (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 86 (1987), S. 4982-4989 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: We present a calculation of the potential energy curves of the 3Σ+u states of the H2 molecule in the region R=1–30 a.u. The features of the correlation diagram are discussed, and a new series of avoided crossings in the region of R〈5 a.u. is predicted. We calculate and analyze the radial couplings which are of interest in the study of the excitation process H(1s)+H(1s)→H(2s,2p)+H(1s). Finally, we introduce a simple analytical model which accounts for the 2 3Σ+u−3 3Σ+u interaction.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.452669
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  • 7
    Digitale Medien
    Digitale Medien
    On the use of adiabatic switching to locate quantized, periodic orbits: Application to bound and reactive multidimensional problems (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 84 (1986), S. 1533-1546 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: We show that the adiabatic switching method can be used to find periodic orbits in nonseparable multidimensional Hamiltonian systems. It is shown that the stable periodic orbits for the fully coupled system can be found by adiabatically propagating periodic orbits from a soluble zero order reference system. A general validity criterion for the technique is presented. The method is successfully tested on several two-dimensional coupled Morse oscillator problems. The most exciting applications are to chemical reactions. We successfully locate trapped, quantized orbits for collinear and three-dimensional models of the H+MuH and H+FH reactions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.450499
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  • 8
    Digitale Medien
    Digitale Medien
    The semiclassical quantization of nonseparable systems using the method of adiabatic switching (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 82 (1985), S. 4611-4632 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: A method for the semiclassical quantization of multidimensional bound systems based on the adiabatic hypothesis is examined. The validity criteria for multidimensional adiabaticity is discussed. It is demonstrated that the quantizing orbits for nonseparable systems can often be obtained by propagating a single trajectory from well defined initial conditions with a time-dependent Hamiltonian for ∼100 periods. Numerical examples using systems with up to five degrees of freedom are presented and show generally excellent results. It is shown that this method can be used to quantize some states using chaotic trajectories.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.448719
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  • 9
    Digitale Medien
    Digitale Medien
    The adiabatic switching of semiclassical wave functions (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 85 (1986), S. 2760-2773 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: The behavior of semiclassical wave functions during adiabatic deformations of the Hamiltonian is studied. A practical technique based on Gaussian wave packet dynamics is presented which allows a semiclassical eigenstate for one Hamiltonian to be adiabatically switched into an eigenstate for a different Hamiltonian. The validity of this technique is established by studying the properties of the Hamilton–Jacobi equation during adiabatic processes. The method is shown to yield good results for several one- and two-dimensional model problems. It is shown that converged semiclassical eigenstates can be obtained even if the trajectories have become chaotic by the end of the switching process.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.451032
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  • 10
    Digitale Medien
    Digitale Medien
    Deterministic diffusion in almost integrable systems (1996)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 6 (1996), S. 519-527 
    Details
    ISSN: 1089-7682
    Quelle: AIP Digital Archive
    Thema: Physik
    Notizen: Diffusion processes are usually associated with randomness in the system. In this paper we show that deterministic diffusion processes can also occur in systems with zero entropy that mimic chaos with any precision without being mathematically chaotic. A random walk model is used to predict the behavior of the diffusion coefficient. © 1996 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.166199
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