Abstract
In the first 11 chapters, to establish the generalized dynamics theory of soft-matter quasicrystals, we used the general concepts from the conservation laws and symmetry breaking principle. Based on that some applications have been successfully demonstrated in Chaps. 7–11 via solving the initial- or boundary- or initial and boundary-condition problems of the governing equations of the dynamics.
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
References
Planck, M.: Ueber irreversible Strahlungsvorgaenge. Ann. Phys. 1, 89–96 (1900)
Einstein, A.: Ueber einen die Erzeugung und Verwandlung des Lichits betreffenden heuristschen Gesichtspunkt. Ann. Phys. 17, 132–148 (1905)
Wang, Z.X.: Statistical Physics. Peking University Press, Beijing, Chinese (2010)
Debye, P.: Die Eigentuemlichkeit der spezifischen Waermen bei tiefen Temperaturen. Arch de Genéve 33(4), 256–258 (1912)
Sommerfeld, A.: Vorlesungen ueber theoretische Physik, Band II, Mechanik der deformierbaren Medium. Verlag Harri Deutsch, Thun. Frankfurt/M (1992)
Born, M., von Kármán, Th.: Zur Theorie der spezifischen Waermen. Physikalische Zeitschrift 14(1), 15–19 (1913); Born, M., Huang, K.: Dynamic Theory of Crystal Lattices. Clarendon Press, Oxford (1954)
ter Harr, D. (ed.): Collected Papers of L D Landau. Pergamon Press, New York (1965)
Anderson, P.W.: Basic Notations of Condensed Matter Physics. Benjamin-Cummings, Menlo-Park (1984)
Lifshitz, M.E., Pitaevskii, L.: Statistical Physics, Part 2. Pergamon, Oxford (1980)
Kittel, C.: Introduction to Solid State Physics, 5th edn. John, New York (1976)
Ren, S.Y.: Electronic State in Crystals of Finite Size. Springer, New York (2017)
Bak, P.: Phenomenological theory of icosahedral incommensurate (“quaisiperiodic”) order in Mn-Al alloys. Phys. Rev. Lett. 54, 1517–1519 (1985)
Bak, P.: Symmetry, stability and elastic properties of icosahedral incommensurate crystals. Phys. Rev. B 32(9), 5764–5772 (1985)
Lubensky, T.C., Ramaswamy, S., Toner, J.: Hydrodynamics of icosahedral quasicrystals. Phys. Rev. B 32(11), 7444–7452 (1985)
Ding, D.H., Yang, W.G., Hu, C.Z., et al.: Generalized elasticity theory of quasicrystals. Phys. Rev. B 48(10), 7003–7010 (1993)
Hu, C.Z., Wang, R.H., Ding, D.H.: Symmetry groups, physical property tensors, elasticity and dislocations in quasicrystals. Rep. Prog. Phys. 63(1), 1–39 (2000)
Hu, C.Z., Ding, D.H., Yang, W.G., Wang, R.H.: Possible two-dimensional quasicystal structure. Phys. Rev. B 49, 9423–9427 (1994)
Fan, T.Y.: Equation system of generalized hydrodynamics of soft-matter quasicrystals. Appl. Math. Mech. 37, 331–347. in Chinese (2016); arXiv:1908.06425 [cond-mat.soft], Oct 15 (2019)
Anderson, P.W.: More is different—broken symmetry and the nature of the hierarchical structure of science. Science 177, 393–396 (1972)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Fan, TY., Yang, W., Cheng, H., Sun, XH. (2022). Re-Discussion on Symmetry Breaking and Elementary Excitations. In: Generalized Dynamics of Soft-Matter Quasicrystals. Springer Series in Materials Science, vol 260. Springer, Singapore. https://doi.org/10.1007/978-981-16-6628-5_12
Download citation
DOI: https://doi.org/10.1007/978-981-16-6628-5_12
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-6627-8
Online ISBN: 978-981-16-6628-5
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)