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md2011-05-note2_Part_8

md2011-05-note2_Part_8 - T C T I Correlations between two...

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Unformatted text preview: T C T I Correlations between two quantities, A and B are measured via the correlation coefficient c AB = h δ A δ B i σ ( A ) σ ( B ) , (47) where σ 2 ( A ) = δ A 2 ens- h A i 2 ens ( σ is the standard deviation), and δ A = A- h A i ens . h δ A δ B i is the covariance of A and B . I Correlation coefficient c AB is always between 0 and 1, values close to 1 corresponding to high correlation. I If A ( t ) and B ( t 1 ) are evaluated at two different times, we obtain the time correlation function c AB ( t ) . I For identical functions c AA ( t ) is called the autocorrelation function and its time integral over t = ... ∞ is the correlation time t A . Notes I These functions are interesting because: I They describe the dynamics of the system , I the time integrals t A can often be related to macroscopic transport coefficients , and I their Fourier transforms ˆ c AA ( ω ) can often be related to experimental spectra ....
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  • Winter '12
  • Kotakoski
  • Fundamental physics concepts, correlation function, Correlation coefficient cAB, correlation function cAB, correlation time tA

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md2011-05-note2_Part_8 - T C T I Correlations between two...

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