Relaxation of classical particles in two-dimensional anharmonic single-well potentials - art. no. 021114

The canonical ensemble relaxation function of a particle in a symmetric anh armonic potential well in D = 1 is known to exhibit slow algebraic behavior [S. Sen, R. S. Sinkovits and S. Chakravarti, Phys. Rev. Lett. 77, 4855 (19 96); R. S. Sinkovits, S. Sen, J. C. Phillips, and S. Chakravarti, Phys. Rev . E 59, 6497 (1999)]. In the present work, we report a study of relaxation of a particle in symmetric and asymmetric quartic anharmonic potential well s of the form V(x,y) = 1/2 (x(2) + Cy-2) + 1/4 (x(2) + Cy-2)(2) in D = 2. T he relaxation in the above system is identical to that in D=1 wells when C= 0 (since it is then a D=1 system) and C=1. However, for 0 < C<1 and for C m uch greater than1. the frequencies associated with well dynamics are strong ly affected and hence the power spectra are altered as a function of C. Our calculations suggest that the exponents of the long-time tails associated with the relaxation processes are insensitive to D. In closing, we comment on the consequences of our analysis for the study of slow dynamics in inter acting many-particle systems that are connected by harmonic springs with th e individual particles in anharmonic potential wells.