Abstract
We describe results concerning the existence proofs of Discrete Breathers (DBs) in the two classes of dynamical systems with optical linear phonons and with acoustic linear phonons. A standard approach is by continuation of DBs from an anticontinuous limit. A new approach, which is purely variational, is presented. We also review some numerical results on intraband DBs in random nonlinear systems. Some non-conventional physical applications of DBs are suggested. One of them is understanding slow relaxation properties of glassy materials. Another one concerns energy focusing and transport in biomolecules by targeted energy transfer of DBs. A similar theory could be used for describing targeted charge transfer of nonlinear electrons (polarons) and, more generally, for targeted transfer of several excitations (e.g. Davidov soliton).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R.T. Birge, H. Sponer, Phys. Rev. 28 (1926) 259–283; J.W. Ellis, Phys. Rev. 33 (1929) 27-36.
A.A. Ovchinnikov, N.S. Erikhman, Usp.Fiz.Nauk 138 (1982) 289–320 and Sov. Phys. Usp. 25 738-755.
Alwyn Scott, Nonlinear Science, Emergence and Dynamics of Coherent Structures, Oxford University Press (1999).
L. Landau, Phys. Z. Sowjetunion 3 (1933) 664.
G.L. Lamb, Elements of Soliton Theory, Pure and Applied Mathematics, J. Wiley & sons, NY, (1982).
A. J. Sievers, S. Takeno (1988) Phys. Rev. Lett. 61 970–973.
R.S. MacKay, S. Aubry, Nonlinearity 7 (1994) 1623–1643.
J.L. Marin, S. Aubry, Nonlinearity 9 (1996) 1501–1528.
R.S. MacKay, J-A. Sepulchre, Physica D 82 (1995) 243–254.
S. Aubry, Physica D103, (1997) 201–250.
J-A. Sepulchre, R.S. MacKay, Nonlinearity 10 (1997) 679–713.
S. Aubry, Ann. Inst. H. Poincaré, Phys. Théor. 68 (1998) 381–420.
R. Livi, M. Spicci, R.S. MacKay, Nonlinearity 10 (1997) 1421–1434.
S. Aubry, G. Kopidakis, V. Kadelburg, preprint submitted to DCDS-B (2001).
S. Flach, K. Kladko, R.S. MacKay, Phys. Rev. Lett. 78 (1997) 1207–1210.
G. Kopidakis, S. Aubry, Physica D 130 (1999) 155–186.
G. Kopidakis and S. Aubry, Phys. Rev. Lett. 84 (2000) 3236–3239; Physica D 139 (2000) 247-275.
G. Kopidakis and S. Aubry, Discrete breathers in realistic models: hydrocarbon structures, Physica B (2001) in press.
R. Papoular, Astronomy and Astrophysics, 359 (2000) 397–404; Numerical simulation of the infrared emission of interstellar dust, to appear in Spectrochimica Acta A (2001).
K.0. Rasmussen, S. Aubry, A.R. Bishop, G.P. Tsironis, Eur. Phys. J. B 15 (2000) 169–175.
K.O. Rasmussen, T. Cretegny, P.G. Kevrekidis and N. Gr0enbech-Jensen, Phys. Rev. Lett. 84 (2000) 3740–3743.
G.P. Tsironis, S. Aubry, Phys. Rev. Lett. 77 (1996) 5225–5228.
A. Bikaki, N.K. Voulgarakis, S. Aubry, G.P. Tsironis, Phys. Rev. E 59 (1999) 1234–1237.
G. Kopidakis and S. Aubry, unpublished.
S. Aubry, G. Kopidakis, A.M. Morgante and G.P. Tsironis, Analytic Conditions for Targeted Energy Transfer between Nonlinear Oscillators or Discrete Breathers, Physica B (2001) in press.
G. Kopidakis, S. Aubry and G.P. Tsironis, Targeted Energy Transfer through Discrete Breathers in Nonlinear Systems, preprint submitted to Phys. Rev. Lett.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Aubry, S., Kopidakis, G. (2001). Aspects of Discrete Breathers and New Directions. In: Abdullaev, F., Bang, O., Sørensen, M.P. (eds) Nonlinearity and Disorder: Theory and Applications. NATO Science Series, vol 45. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0542-5_8
Download citation
DOI: https://doi.org/10.1007/978-94-010-0542-5_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-0192-5
Online ISBN: 978-94-010-0542-5
eBook Packages: Springer Book Archive