2018/06/11 by Hoover, Wm. G., Hoover, Carol G.
#Classical Physics (physics.class-ph) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.1806.03797
The one-dimensional ϕ4 Model generalizes a harmonic chain with nearest-neighbor Hooke's-Law interactions by adding quartic potentials tethering each particle to its lattice site. In their studies of this model Kenichiro Aoki and Dimitri Kusnezov emphasized its most interesting feature : because the quartic tethers act to scatter long-wavelength phonons, ϕ4 chains exhibit Fourier heat conduction. In his recent Snook-Prize work Aoki also showed that the model can exhibit chaos on the three-dimensional energy surface describing the two-body two-spring chain. That surface can include \it at least two distinct chaotic seas. Aoki pointed out that the model typically exhibits different kinetic temperatures for the two bodies. Evidently few-body ϕ4 problems merit more investigation. Accordingly, the 2018 Prizes honoring Ian Snook (1945-2013) will be awarded to the author(s) of the most interesting work analyzing and discussing few-body ϕ4 models from the standpoints of dynamical systems theory and macroscopic thermodynamics, taking into account the model's ability to maintain a steady-state kinetic temperature gradient as well as at least two coexisting chaotic seas in the presence of deterministic chaos.