Local Dynamics in an Infinite Harmonic Chain

Abstract

By the method of recurrence relations, the time evolution in a local variable in a harmonic chain is obtained. In particular, the autocorrelation function is obtained analytically. Using this result, a number of important dynamical quantities are obtained, including the memory function of the generalized Langevin equation. Also studied are the ergodicity and chaos in a local dynamical variable.

Keywords

• recurrence relations
• harmonic chain
• local dynamics
• ergodicity
• chaos