References

Primary Publications

The theoretical framework implemented by this package is developed in the following two papers:

[He2024]

H. He, W. Chen, et al., “Generalized two-time correlation for study of nonequilibrium dynamics with X-ray photon correlation spectroscopy,” Proc. Natl. Acad. Sci. U.S.A. 121 (48), e2401162121 (2024). doi:10.1073/pnas.2401162121

Introduces the transport coefficient \(J(t)\), the two-time correlation framework, and the connection between microscopic velocity statistics and measurable scattering correlations. Derives the integral formulation and the power-law parameterization.

[He2025]

H. He, W. Chen, et al., “Multi-component heterodyne XPCS for extracting flow dynamics under nonequilibrium conditions,” Proc. Natl. Acad. Sci. U.S.A. 122, e2514216122 (2025). doi:10.1073/pnas.2514216122

Extends the theory to multi-component heterodyne detection. Derives the N-component correlation (SI Eq. S-94), the two-component specialization (SI Eqs. S-95/S-98), and demonstrates velocity extraction from cross-correlation oscillations.

BibTeX Entries

@article{He2024,
  author  = {He, Hongrui and Chen, Wei and others},
  title   = {Generalized two-time correlation for study of
             nonequilibrium dynamics with {X}-ray photon
             correlation spectroscopy},
  journal = {Proceedings of the National Academy of Sciences},
  volume  = {121},
  number  = {48},
  pages   = {e2401162121},
  year    = {2024},
  doi     = {10.1073/pnas.2401162121},
}

@article{He2025,
  author  = {He, Hongrui and Chen, Wei and others},
  title   = {Multi-component heterodyne {XPCS} for extracting
             flow dynamics under nonequilibrium conditions},
  journal = {Proceedings of the National Academy of Sciences},
  volume  = {122},
  pages   = {e2514216122},
  year    = {2025},
  doi     = {10.1073/pnas.2514216122},
}

Related References

[SiegertRelation]

A. J. F. Siegert, “On the fluctuations in signals returned by many independently moving scatterers,” MIT Radiation Laboratory Report No. 465 (1943).

Original derivation of the Siegert relation connecting first- and second-order correlation functions for Gaussian random fields.

[GreenKubo]

M. S. Green, “Markoff random processes and the statistical mechanics of time-dependent phenomena. II. Irreversible processes in fluids,” J. Chem. Phys. 22, 398 (1954). R. Kubo, “Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems,” J. Phys. Soc. Japan 12, 570 (1957).

The Green-Kubo relations connecting transport coefficients to time-integrated velocity autocorrelation functions.

[BerneXPCS]

B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Wiley, 1976).

Standard reference for the theory of dynamic light scattering, including homodyne and heterodyne detection geometries.

[SuttonXPCS]

M. Sutton, “A review of X-ray intensity fluctuation spectroscopy,” C. R. Physique 9, 657 (2008).

Comprehensive review of XPCS methodology, coherence requirements, and data analysis procedures.