Non-Markovian Two-Time Correlation Dynamics and Nonergodicity

The two-time correlation functions of the coordinate and velocity of a non-Markovian harmonic particle are derived analytically. They are decomposed into the components of differences between the initial variances and the equilibrium of the particle; in particular, the dependence of a random force on the initial preparation of the system is included. Using those expressions, we simultaneously investigate nonstationary, nonergodic, and nonequilibrium features of a forced system. It is demonstrated that the result of combining the oscillating relaxation and the initial preparation-dependent noise leads to breakdown of both ergodicity and equilibration of a forced system. The finite-size effect of a coupled-oscillator-chain heat bath is also discussed.