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Volumn 131, Issue , 2005, Pages 243-375

Classical description of nonadiabatic quantum dynamics

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EID: 32544458965     PISSN: 00652385     EISSN: None     Source Type: Book Series    
DOI: 10.1002/0471739464.ch5     Document Type: Review
Times cited : (227)

References (296)
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    • For the applications considered, it was found that it virtually makes no difference whether the phase q is sampled from the intervall [0,2π] or chosen as q = 0 for each trajectory.
    • For the applications considered, it was found that it virtually makes no difference whether the phase q is sampled from the intervall [0,2π] or chosen as q = 0 for each trajectory.
  • 204
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    • See, for example, the discussions in Ref. 18 and in L. E. Ballentine, Y. Yang, and J. P. Zibin, Phys. Rev. A 50, 2854 (1994).
    • See, for example, the discussions in Ref. 18 and in L. E. Ballentine, Y. Yang, and J. P. Zibin, Phys. Rev. A 50, 2854 (1994).
  • 205
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    • 12.
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  • 209
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    • personal communication
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    • This general feature of the stochastic scheme may cause convergence problems. For example, consider a situation in which the molecular system is predominately in a single state, say ρ11. Although the expectation values of the population P2, trρ22 and the corresponding coherences are zero, there are the same number of random walkers in these states which need to cancel themselves in the phase average
    • 22 and the corresponding coherences are zero, there are the same number of random walkers in these states which need to cancel themselves in the phase average.
  • 217
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    • 6 random walkers would be required.
    • 6 random walkers would be required.
  • 223
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    • For a general discussion and an overview of existing methods, see, for example
    • For a general discussion and an overview of existing methods, see, for example, Y. Guo, D. L. Thompson, and T. D. Sewell, J. Chem. Phys. 104, 576 (1996).
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    • Guo, Y.1    Thompson, D.L.2    Sewell, T.D.3
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    • Ph.D. thesis, University of Freiburg, unpublished
    • U. Müller, Ph.D. thesis, University of Freiburg, unpublished (1999).
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    • For a nonadiabatic system with spin-orbit interaction, the validity of the semiclassical approximation (based on the spin-coherent state representation) has been discussed in detail in
    • For a nonadiabatic system with spin-orbit interaction, the validity of the semiclassical approximation (based on the spin-coherent state representation) has been discussed in detail in Ref. 147.
    • , vol.147
    • Ref1
  • 267
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    • unpublished results
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    • Mixed quantum-classical description of the dynamics at conical intersections
    • W. Domcke, D. R. Yarkony, and H. Köppel, eds, World Scientific, Singapore
    • G. Stock and M. Thoss, Mixed quantum-classical description of the dynamics at conical intersections, in Canonical Intersections, W. Domcke, D. R. Yarkony, and H. Köppel, eds., World Scientific, Singapore, 2004.
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  • 270
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    • For a discussion of the nonunitarity of the semiclassical approximation in the context of nonadiabatic dynamics, see, for example, Ref. 100
    • For a discussion of the nonunitarity of the semiclassical approximation in the context of nonadiabatic dynamics, see, for example, Ref. 100.
  • 278
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    • Wang et al. have recently reperformed the calculation for the 24-mode pyrazine model employing an improved filtering technique, thereby reducing the number of trajectories required to obtain convergence by almost two orders of magnitude [122
    • Wang et al. have recently reperformed the calculation for the 24-mode pyrazine model employing an improved filtering technique, thereby reducing the number of trajectories required to obtain convergence by almost two orders of magnitude [122].
  • 287
    • 49249135985 scopus 로고    scopus 로고
    • It is noted that in the results of Suzuki's propagator given in Fig. 7 of Ref. 100, an incorrect normalization factor was used, which resulted in a strong deviation of the overall magnitude of the autocorrelation function from the quantum-mechanical result.
    • It is noted that in the results of Suzuki's propagator given in Fig. 7 of Ref. 100, an incorrect normalization factor was used, which resulted in a strong deviation of the overall magnitude of the autocorrelation function from the quantum-mechanical result.


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