Generation and application of non-ergodic noise

When using the noise of n-order time derivative as an internal thermal noise to drive a generalized Langevin equation, if the nonergodicty strength of the noise satisfies b not equal 0 and the system is in thermal equilibrium, then the stationary velocity variable of the system can be used as a non-ergodic noise. The spectra of the non-ergodic noise is infinite at zero frequency. The one-dimensional semi-unbounded coupled harmonic oscillator chains connected with the gas molecules act as the non-ergodic noise, which is an example of non-ergodic noise. Finally regarding the non-ergodic noise as an external noise to drive the particles in the titled periodic potential, it is found that there appears superballistic diffusion with the effective diffusion index exceeding a ballistic value of 2. It is also found that the velocity distribution of the system displays two motion states, the "locked state" and the "running state". And in the "running state" there occurs a bimodal phenomenon, which is a relatively new phenomenon.