Generalized Langevin equation approach for atom/solid-surface scattering: General formulation for classical scattering off harmonic solids

The Journal of Chemical Physics

Volumn 64, Issue 6, 1976, Pages 2375-2388

  Adelman, S A ^a   Doll, J D ^b  

^a PURDUE UNIVERSITY   (United States)

^b STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 36749113534     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.432526     Document Type: Article

References (54)

1. See, for example
2. See, for example
3. These are, respectively, quantum and classical S-matrix calculations for rigid lattice models.
4. This restriction can be easily removed.
5. This is conveniently accomplished by Laplace transforming Eqs. (2.4) as in Ref. 9.
6. Here and below we use the convention that the Laplace transform of an arbitrary function [formula omitted] will be denoted by [formula omitted] i.e., [formula omitted]
7. See, for example
8. Equations (2.6) and (2.10) give a formulation of lattice dynamics which is particularly convenient for our problem. There are other possible formulations. For an overall review of lattice dynamics see
9. for example
10. Langevin equations for lattice particles were derived using the Mori formalism (Ref. 12) by
11. Fokker-Planck Equations were considered by
12. For stationary random processes [formula omitted] see Ref. 11.
13. See, for example, Ref. 11.
14. For recent work see
15. The effective frequency of Eq. (4.7) when specialized to the case of a single primary zone lattice atom can be shown to be equal to the characteristic frequency appearing in N. B. Slater’s theory of unimolecular decay described in
16. See comments by F. Goodman, Ref. 14.
17. The Debye approximation has been used by the authors of Ref. 2.
18. See Maradudin et al., Ref. 20.
19. Such casual treatment of stochastic equations does not always give correct results; e.g., see Ref. 26.
20. general the number of sample points increases as the Nth power where N is the number of atoms in the heat bath.