Question

1. Question : • 1) When you speak in lecture of "anharmonic motion" is that the same as the "random" motion that Duane 7.1 speaks of, or are they not necessarily the same thing?

2. Autocorrelation Functions Measures the correlation between successive events: From numeric simulations, one has to make the integral into a sum We often normalize as well by y(0)y(0). This is a two-point auto-correlation function. The most commonly used one, but not the only one.

3. Autocorrelation Functions Three-point autocorrelation function: One can generalize to multiple-point autocorrelation functions Not commonly used for simulation analysis, but some nonlinear spectroscopies measure multi-point correlation functions

4. Auto-correlation of fluctuations Positional auto-correlation function of the fluctuations in x,y,z of the C2 atom of Gua10 in a NAMD simulation of mismatched-DNA bound to the MutS complex

5. Cross-correlation Functions Measures the correlation between successive different events: From numeric simulations, one has to make the integral into a sum This is a two-point cross-correlation function.

6. Cross-correlation of fluctuations Usually one wants to know how two {or more} quanitities fluctuate together The cross-correlation function of the fluctuations This is often referred to as the Cross-correlation function

7. Correlation and Covariance The zero-time component {equal-time component} is the correlation. Note: No dynamical information! Properly normalized, this becomes the covariance. Note: No dynamical information!

8. Cross-correlation of fluctuations Positional cross-correlation function of the fluctuations in x,y,z of the C2 atom of Gua10 and Thy 27 in a NAMD simulation of mismatched-DNA bound to the MutS complex

9. Cross-correlation of fluctuations Positional cross-correlation function of the fluctuations in x,y,z of the C2 atom of Gua10 and CZ of Phe 36A in a NAMD simulation of mismatched-DNA bound to the MutS complex

10. Applications of {Quantum} Correlation Functions Kinetic Theory: where the correlation function is a flux- autocorrelation function Spectroscopy: observables can often be written in terms of fourier transforms of correlation functions where the correlation function is a transition dipole or real dipole autocorrelation function depending on the spectroscopy

11. Applications of Correlation Functions Kinetic Theory: Transport processes Frictional damping terms from correlation functions of position