[Ifeffit] Time reversibility of multiple scattering paths

[Scott Calvin]

Hi David,

The TS path in this example, when reversed, is the identical path. A straightforward enumeration of paths would only list it once.

The DS paths would be listed twice in the enumeration: M — M(1) — M(4) — M and M — M(4) — M(1) — M. Those two paths have identical scattering characteristics, and thus could be replaced by a single path with degeneracy two.

In other words, to find degeneracy, list every possible sequence of scattering. Paths that have identical scattering properties may be grouped together and replaced by a single representative with degeneracy equal to the number of instances. If you think about it that way, the answer to your question becomes evident.

Best,

Scott Calvin
Lehman College

> On Nov 18, 2016, at 6:03 AM, Inwood D. <D.Inwood at soton.ac.uk> wrote:
> 
> Hi All,
>  
> I’ve just been reading the paper with the following reference:
>  
> Nashner, M. S.; Frenkel, A. I.; Adler, D. L.; Shapley, J. R.; Nuzzo, R. G. Structural Characterization of Carbon-Supported Platinum - Ruthenium Nanoparticles from the Molecular Cluster. J. Am. Chem. Soc. 1997, 7863, 7760–7771.
>  
> In particular I was interested about the data analysis section on page 7763 (footnote 32) where the authors talk about time reversibility of multiple scattering paths. It is mentioned that the collinear DS path, in the fcc structure, (M – M(1) – M(4) – M) is time reversed, so has twice the degeneracy, but that the collinear TS path (M – M(1) – M(4) – M(1) – M) is not time reversed.
>  
> Why is the DS path time reversible, but not the TS path despite the apparent ‘symmetry’ of the TS path? What makes a scattering path time reversible? Does time reversibility only apply to collinear paths or can it also apply to triangular paths as well?
>  
> Thanks for your help,
>  
> David
>  
> David W Inwood
> PhD Researcher
> Chemistry
> University of Southampton
> Southampton, UK
> SO17 1BJ
>  
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