The dynamic structure factor (DSF) is a key concept in condensed matter physics, particularly in studies of materials and collective excitations such as phonons, magnons, and other quasiparticles. It provides information about the microscopic dynamics of a system, including how density fluctuations evolve over time. Mathematically, the dynamic structure factor \( S(\mathbf{q}, \omega) \) is defined in terms of the Fourier transform of the time-dependent density-density correlation function.
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The dynamic structure factor is the space-time Fourier transform of an equilibrium two-point correlation function. It resolves fluctuations by angular frequency and wavevector and is related to the dissipative part of a retarded Green function by the Fluctuation-dissipation theorem.