Abstract
In this essay, we first sketch the development of ideas on the extraordinary dynamics of integrable classical nonlinear and quantum many body Hamiltonians. In particular, we comment on the state of mathematical techniques available for analyzing their thermodynamic and dynamic properties.Then, we discuss the unconventional finite temperature transport of integrable systems using as example the classical Toda chain and the toy model of a quantum particle interacting with a fermionic bath in one dimension; we focus on the singular long time asymptotic of current-current correlations, we introduce the notion of the Drude weight and we emphasize the role played by conservation laws in establishing the ballistic character of transport in these systems.
Similar content being viewed by others
REFERENCES
N. J. Zabusky and M. D. Kruskal, Phys. Rev. Lett. 15, 240 (1965).
C. S. Gardner, J. M. Greene, M. D. Kruskal and R. M. Miura, Phys. Rev. Lett. 19, 1095 (1967).
“Optical solitons: theoretical challenges and industrial perspectives”, editors: V.E. Zakharov and S. Wabnitz, Les Houches Workshop, Springer (1998).
“Quantum Inverse Scattering Method and Correlation Functions”, V.E. Korepin, N.M. Bogoliubov and A.G. Izergin, Cambridge Univ. Press (1993).
H. Castella, X. Zotos, P. Prelovšek, Phys. Rev. Lett. 74, 972 (1995).
M. Toda, “Theory of Nonlinear Lattices”, Springer Series in Solid-State Sciences 20, Springer-Verlag, (1981).
H. Flaschka, Phys. Rev. B9, 1924 (1974).
M. Henon, Phys. Rev. B9, 1921 (1974).
V. Muto, A.C. Scott and P.L. Christiansen, Physica D44, 75 (1990).
See for instance: T. Schneider and E. Stoll, Phys. Rev. Lett. 45, 997 (1980); A. Cuccoli et al., Phys. Rev. B47, 7859 (1993); N. Theodorakopoulos and M. Peyrard, Phys. Rev. Lett. 83, 2293 (1999).
C. Giardina et al., Phys. Rev. Lett. 84, 2144 (1998).
See however the system analyzed in, M. Garst and A. Rosch, Eur. Lett. 55, 66 (2001).
P. Mazur, Physica 43, 533 (1969); M. Suzuki, Physica 51, 277 (1971).
J.A. McLennan, “Introduction to non equilibrium statistical mechanics”, Prentice-Hall Advanced Reference Series, (1989).
Basically equivalent to the entropic component, N.W. Ashcroft and N.D. Mermin, “Solid State Physics”, Holt, Rinehart and Winston, p. 253 (1976).
X. Zotos, F. Naef and P. Prelovšek, Phys. Rev. B55, 11029 (1997).
F.G. Mertens and H. Büttner, Phys. Lett. 84A, 335 (1981).
W. Kohn, Phys. Rev. A171, 133 (1964).
J. B. McGuire, J. Math. Ph. 6, 432 (1965); C. N. Yang, Phys. Rev. Lett. 19, 1312 (1967).
S. Fujimoto and N. Kawakami, J. Phys. A. 31, 465 (1998).
S. Fujimoto, J. Phys. Soc. Jpn. 68, 2810 (1999).
X. Zotos, Phys. Rev. Lett. 82, 1764 (1999).
K. Damle and S. Sachdev, Phys. Rev. B57, 8307 (1998).
T. Giamarchi and A. J. Millis, Phys. Rev. B46, 9325 (1992).
A. Rosch and N. Andrei, Phys. Rev. Lett. 85, 1092 (2000).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zotos, X. Ballistic Transport in Classical and Quantum Integrable Systems. Journal of Low Temperature Physics 126, 1185–1194 (2002). https://doi.org/10.1023/A:1013827615835
Issue Date:
DOI: https://doi.org/10.1023/A:1013827615835