A system consisting of a great number of interacting particles takes on collective properties that are manifested in the coordinated movement of all the particles in the system. This motion is described in classical mechanics as the propagation in the system of a set of waves for “collective degrees of freedom,” which depend on the coordinates of all the particles in the system. Such waves may exchange energy (that is, interact with one another); the interactions are called collective.
In quantum theory, excitation of collective degrees of freedom or their corresponding waves is regarded as the creation of quasi-particles, and collective interactions are regarded as the interactions between such quasiparticles. For example, in a crystal lattice the normal oscillatory mode of the lattice’s atoms—or, in quantum language, phonons—corresponds to the collective degrees of freedom. All the atoms of the lattice take part in the processes of interaction among phonons; the collective nature of the interaction is manifested in this.
Another example of collective interactions is the interaction between spin waves (magnons) in ferromagnets. The interaction between quasiparticles of different physical nature, such as magnons with phonons, is also considered a collective interaction.
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Ziman, J. Printsipy teorii tverdogo tela. Moscow, 1966. (Translated from English.)
White, R. M. Kvantovaia teoriia magnetizma. Moscow, 1972. (Translated from English.)
Bohm, D. Obshchaia teoriia kollektivnykh peremennykh. Moscow, 1964. (Translated from English.)
D. N. ZUBAREV