When Is a One-Dimensional Lattice Small?

C. Y. Lin; S. N. Cho; C. G. Goedde; S. Lichter

doi:10.1103/PhysRevLett.82.259

When Is a One-Dimensional Lattice Small?

C. Y. Lin, S. N. Cho, C. G. Goedde, and S. Lichter

Phys. Rev. Lett. 82, 259 – Published 11 January 1999

Abstract

While the use of continuum approximations to describe systems consisting of many molecules is well established, it is not known how such approximations fail as the number of molecular components decreases. We study the one-dimensional Fermi-Pasta-Ulam chain in order to determine the critical value of the system size below which the system's behavior deviates from the continuum limit, allowing us to delineate between “small” and “large” systems and define these terms precisely. For this system, the distinction between small and large is correlated with the appearance of an instability of the chain.

Received 13 July 1998

DOI:https://doi.org/10.1103/PhysRevLett.82.259

Authors & Affiliations

C. Y. Lin¹, S. N. Cho², C. G. Goedde^2,*, and S. Lichter^1,†

¹Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208
²Department of Physics, DePaul University, 2219 North Kenmore Avenue, Chicago, Illinois 60614

^*Electronic address: goedde@cascade.phy.depaul.edu
^†Electronic address: s-lichter@nwu.edu