Relaxation of classical particles in twodimensional anharmonic singlewell potentials
Abstract
The canonical ensemble relaxation function of a particle in a symmetric anharmonic 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 (1996); 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 wells of the form V(x,y)=12 (x^{2}+Cy^{2})+14 (x^{2}+Cy^{2})^{2} in D=2. The 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>>1, the frequencies associated with well dynamics are strongly affected and hence the power spectra are altered as a function of C. Our calculations suggest that the exponents of the longtime 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 interacting manyparticle systems that are connected by harmonic springs with the individual particles in anharmonic potential wells.
 Publication:

Physical Review E
 Pub Date:
 February 2001
 DOI:
 10.1103/PhysRevE.63.021114
 Bibcode:
 2001PhRvE..63b1114V
 Keywords:

 05.40.a;
 65.90.+i;
 Fluctuation phenomena random processes noise and Brownian motion;
 Other topics in thermal properties of condensed matter