ABSTRACT
This chapter introduces the reader to the proper language in which to express with precision results of both theory and experiment concerning the response of a many-particle system to macroscopic and microscopic external probes. It shows why the Landau theory is rigorous in the long wavelength limit: as we pointed out earlier, the Landau theory is equivalent to neglecting multipair excitations in the calculation of the response function. The chapter suggests that the Landau theory succeeds because in the limit of small q and ω, the contribution of multipair excitations is usually negligible. By studying the structure of the linear response function, one may describe explicitly the transition from the collisionless high-frequency regime (where the system response is essentially microscopic), to the low-frequency hydrodynamic regime (where the response is governed by macroscopic average laws). The chapter considers a simple physical example of probe-liquid interaction, the inelastic scattering of an external particle beam by a neutral quantum liquid.
