Correlation Analysis¶

Computing autocorrelation functions and spectral analysis for cavity-coupled systems.

Dipole Autocorrelation ¶

Definition:

\[C(t) = \langle \vec{D}(t') \cdot \vec{D}(t'+t) \rangle\]

Used for computing IR spectra and relaxation times.

Fourier transform:

\[I(\omega) \propto \omega^2 \int_0^\infty C(t) e^{-i\omega t} dt\]

See Analysis Tools for implementation details.

For cavity mode analysis:

\[C_q(t) = \langle q(t') q(t'+t) \rangle\]

Reveals cavity mode dynamics and damping.