Mermin

Aschroft N W and Mermin N D 1976 Solid State Physics (New York Hoit, Rinehart and Winston)... 

Fig. 3.8 Some basic Bravais lattices (a) simple cubic, (b) body-centred cubic, (c) face-centred cubic and (d) simple hexagonal close-packed. (Figure adapted in part from Ashcroft N V and Mermin N D 1976. Solid State Physics.

That is, Ci 2(t + P) = Ci,2Wexp( j3e). In fact, when the temperature is less than the separation between the two lowest energy levels of the bath, the latter can be approximated by a set of two-level systems [Caldeira and Leggett 1983 Mermin 1991],... 

Therefore, at extremely low temperatures one may equally choose between TLS and say oscillator bath. The latter is usually supposed to be simpler to handle, but the TLS bath model, apart from its apparent relevance for glass theory, has some very attractive features [Mermin 1991 Suarez and Silbey 1991b Shimshoni and Cefen 1991]. 

Here we briefly summarize some major results of solid state theory that are relevant for understanding the behavior of adsorption on surfaces. For a more detailed description please consult excellent books such as S. Elliot, The Physics and Chemistry of Solids (1998), Wiley Sons, New York N. Ashcroft and N.D Mermin, Solid... 

Ashcroft, N. W., Mermin, N. D., Solid State Physics, Harcourt Brace College Publishers, Fort Worth, TX (1976). 

Mermin s "generalised crystallography" works primarily with reciprocal space notions centered around the density and its Fourier transform. Behind the density there is however a wave function which can be represented in position or momentum space. The wave functions needed for quasicrystals of different kinds have symmetry properties - so far to a large extent unknown. Mermin s reformulation of crystallography makes it attractive to attempt to characterise the symmetry of wave functions for such systems primarily in momentum space. 

In the next setion we review some key concepts in Mermin s approach. After that we summarise in section III some aspects of the theory of (ordinary) crystals, which would seem to lead on to corresponding results for quasicrystals. A very preliminary sketch of a study of the symmetry properties of momentum space wave functions for quasicrystals is then presented in section IV. 

As stressed by Mermin and collaborators [9 - 18] it is far too restrictive to define the structural indistinguishability of two mesoscopically homogeneous materials with reference to identical densities. Instead of the densities themselves one should study the properties of the correlationfunctions,... 

Two densities P(r) and p (r) are said to be indistinguishable if all their correlation functions and c are identical. As shown by Mermin and collaborators their Fourier transforms... 

From this group compatibility condition Mermin and his collaborators have derived both all the "ordinary" crystallographic and the quasicrystallographic space groups. 

One of the main points in the papers by Mermin and his collaborators [9 - 18] is the insistence on the primacy of reciprocal space. The properties of the Fourier transform of the density rather than the density itself determine those properties which are of importance for "generalized" crystallography. As pointed out by Mermin that point view was stressed in a paper by Bienenstock and Ewald already in 1962 [26]. 

Mermin [9, 18] has given a recipe for the construction of a set of Fourier components for a density characterised by a certain space group. The space group is then specified by a point group G, a lattice of wave vectors in the sense discussed above, and a set of phase... 

What has been sketched here is obviously just the bare framework of a general investigation of the sy mmetry properties of momentum spaee funetions in quasieiy stals. With all the information available in the papers by Mermin and eollaborators it should however be a very tempting enterprise to go ahead along the lines sketehed and learn about the details of the symmetry properties of those wave functions - both in momentum and in positition space - whieh will be needed in quasiperiodic extended systems. 

N.D. Mermin, in Proceedings of the International Workshop on Modulated Crystals. Bilbao, Spain, World Scientific, Singapore 1991. 

N. Ashcroft and N. Mermin, Solid State Physics, Holt, Rinehart and Winston, New York, 1977. 

Ashcroft, N.W. and Mermin, N.D. (1976) Solid State Physics, Saunders College, Philadephia. 

Hilborn, E.D., Mermin, J.H., Mshar, P.A., Hadler, J.L., Voetsch, A., Wojtkunski, C., Swartz, M., Mshar, R., Lambert-Fair, M.-A., Farrar, J.A., Glynn, K. and Slutsker, L. (1999) A multistate outbreak of Escherichia coli 0157 H7 infections associated with consumption of mesclun lettuce . Archives of Internal Medicine, 159, 1758-1764. 

N.W. Ashcroft, N.D. Mermin Solid State Physics, Saunders College Publishing, Philadelphia (1976)... 

Good introductions into lattice structures and single crystal surfaces can be found in N. Ashcroft and N. Mermin, Solid State Physics, Holt, Rinehart and Winston, 1976 A. Zangwill, Physics at Surfaces Cambridge University Press, 1988 C. Kittel, Introduction to Solid State Physics, J. Wiley and Sons, New York, 1986 G. Somorjai, Surface Chemistry and Catalysis, Wiley-Interscience, New York, 1994. 

Ashcroft NW, Mermin ND (1976) Solid state physics. Saunders College, Philadelphia... 

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