Abstract
We enumerate simple periodic orbits for the well-known Fermi-Pasta-Ulam (FPU) problem. Using these solutions as simple modes for the problem, we construct quantum solutions of the corresponding problem. These studies present a natural generalization of the concept of phonon in the nonlinear realm.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. Bruus, K. Flensberg, Many-body Quantum Theory in Condensed Matter Physics (Oxford University Press, Oxford, 2004)
J. Hoppe, Lectures on Integrable Systems (Springer, Berlin, 1992)
F. Cooper, A. Khare, U. Sukhatme Supersymmetry in Quantum Mechanics (World Scientific, Singapore, 2001)
G. Auberson, S.R. Jain, A. Khare, J. Phys. A 34, 695 (2001)
S.C. Johnson, T.D. Gutierrez, Am. J. Phys. 70, 227 (2002)
J. Ford, Phys. Rep. 213, 271 (1992)
C.M. Bender, S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (Springer, Berlin, 2010)
C. Antonopoulos, T. Bountis, Phys. Rev. E 73, 056206 (2006)
A.C. Dixon, The Elementary Properties of the Elliptic Functions (Cornell University library, 1894)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sonone, R.L., Jain, S.R. Nonlinear normal modes and quanta in the β Fermi-Pasta-Ulam lattice. Eur. Phys. J. Spec. Top. 222, 601–608 (2013). https://doi.org/10.1140/epjst/e2013-01865-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2013-01865-4