Abstract
We study the time scale T to equipartition in a lattice of N masses coupled by quartic nonlinear (hard) springs (the Fermi-Pasta-Ulam β model). We take the initial energy to be either in a single mode γ or in a package of low-frequency modes centered at γ and of width δγ, with both γ and δγ proportional to N. These initial conditions both give, for finite energy densities a scaling in the thermodynamic limit (large N), of a finite time to equipartition which is inversely proportional to the central mode frequency times a power of the energy density A theory of the scaling with is presented and compared to the numerical results in the range
- Received 2 June 1999
DOI:https://doi.org/10.1103/PhysRevE.60.3781
©1999 American Physical Society