Abstract
Macroscopic variables, necessary for a useful dynamical description of many condensed phases, are discussed. The nature of these macroscopic variables, their origin and their implications for the dynamics are considered. The somewhat special case of phasmids is treated separately.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. D. Landau and E. M. Lifshitz, “Fluid Mechanics” (Pergamon, London), 1959.
L. P. Kadanoff and P. C. Martin, Ann. Phys. 24, 419 (1963).
P. Hohenberg and P. C. Martin, Ann. Phys. 34, 291 (1965).
I. M. Khalatnikov, “Introduction to the Theory of Superfluidity” (Benjamin, New York, 1965).
B. I. Halperin and P. Hohenberg, Phys. Rev. 188, 898 (1968).
R. Graham, Phys. Rev. Lett. 23, 1431 (1974).
R. Graham and H. Pleiner, Phys. Rev. Lett. 24, 792 (1975).
R. Graham and H. Pleiner, J. Phys. C9, 279 (1976).
M. Liu,. Phys. Rev. Lett. 43, 1740 (1979).
P. C. Martin, O. Parodi and P. S. Pershan, Phys. Rev. A6, 2401 (1972).
D. Forster, Ann. Phys. 84, 505 (1974).
T. C. Lubensky, Phys. Rev. A6, 452 (1972).
H. Brand and H. Pleiner, J. Physique 41, 553 (1980).
H. Pleiner and H. Brand, J. Physique Lett. 41, L491 (1980).
H. Brand and H. Pleiner, Phys. Rev. A24, 2777 (1981).
H. Pleiner and H. Brand, Phys. Rev. A25, 995 (1982).
H. Brand and H. Pleiner, J. Physique 45, 563 (1984).
H. Pleiner and H. R. Brand, Phys. Rev. A29, 911 (1984).
Except the angular momentum density, which is dynamically not an independent variable (cf. Ref. 10).
Except when long-ranged forces are present.
D. Forster, “Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions” (Benjamin, Reading, 1975).
F. Jähnig and H. Schmidt, Ann. Phys. 71, 129 (1972).
W. L. McMillan, Phys. Rev. A9, 1720 (1974).
J. Swift, Phys. Rev. A13, 2274 (1976).
M. Liu, Phys. Rev. A19, 2090 (1979).
B. Julia, and G. Toulouse, J. Physique Lett. 40, L395 (1979).
I. E. Dzyaloshinskii and G. E. Volovik, Ann Phys. 125, 67 (1980).
K. Kawasaki, Ann. Phys. 154, 319 (1984).
H. R. Brand and K. Kawasaki, J. Phys. A17, L905 (1984).
Usually rotational symmetry; but if a field is modulated in space, it also breaks translational symmetry.
P. G. de Gennes, “The Physics of Liquid Crystals” (Clarendon, Oxford, 1974).
H. Pleiner, J. Phys. C10, 4241 (1977).
D. R. Nelson and B. I. Halperin, Phys. Rev. B21, 5312 (1980).
R. Pindak, D. E. Moncton, S. C. Davey and J. W. Goodby, Phys. Rev. Lett. 46, 1135 (1981).
J. J. Benattar, F. Moussa and M. Lambert, J. Chim. Phys. 80, 99 (1983).
J. D. Brock, A. Aharony, R. J. Birgeneau, K. W. Evans-Lutterodt, J. D. Litster, P. M. Horn, G. B. Stephenson and A. R. Tajbakhsh, Phys. Rev. Lett. 57, 98 (1986).
H. Pleiner, Mol. Cryst. Liq. Cryst. 114, 103 (1984).
H. Pleiner and H. R. Brand, Phys. Rev. A29, 911 (1984).
This definition is not restricted to translational broken symmetries.
Except near the smectic A-nematic phase transition (ref. 25).
J. Prost in “Liquid Crystals of One- and Two-Dimensional Order,” W. Helfrich and G. Heppke, eds. (Springer, Berlin, 1980), p. 125.
This definition avoids the physically somewhat unsatisfactory distinction between rational and irrational numbers; on the other hand, it may be difficult to distinguish between no interaction and extremely small interaction.
J. Prost and P. Barois, J. Chim Phys. 80, 65 (1983).
H. R. Brand and H. Pleiner (to be published).
H. Brand and P. Bak, Phys. Rev. A27, 1062 (1983).
In that case, I would call these systems commensurate.
The real and imaginary parts of the dispersion relation vanish with equal power of the wave vector.
The masses of the different atomic species are different.
J. D. Axe and P. Bak, Phys. Rev. B26, 4963 (1982).
D. Schechtman, I. Blech, D. Gratias and J. W. Cahn, Phys. Rev. Lett. 53, 1951 (1984).
P. Bak, Phys. Rev. Lett. 54, 1517 (1985).
T. C. Lubensky, S. Ostlund, S. Ramaswamy, P. J. Steinhardt, and J. Toner, Phys. Rev. Lett. 54, 1520 (1985).
N. D. Mermin and S. M. Troian, Phys. Rev. Lett. 54, 1524 (1985).
M. Kleman, Y. Gefen and Y. Pavlovitch, Europhys. Lett. 1, 61 (1986).
The latter is proposed in T. Janssen, these proceedings.
J. Malthete, A. M. Levelut and Nguyen Hu Tinh, J. Physique Lett. 46, L876 (1985).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Plenum Press, New York
About this chapter
Cite this chapter
Pleiner, H. (1987). Macroscopic Variables in Commensurate and Incommensurate Condensed Phases, Quasicrystals and Phasmids. In: Scott, J.F., Clark, N.A. (eds) Incommensurate Crystals, Liquid Crystals, and Quasi-Crystals. NATO ASI Series, vol 166. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-0184-5_22
Download citation
DOI: https://doi.org/10.1007/978-1-4757-0184-5_22
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-0186-9
Online ISBN: 978-1-4757-0184-5
eBook Packages: Springer Book Archive