By V. N. Popov, V. S. Yarunin (auth.)
Material debris, electrons, atoms, molecules, engage with each other through electromagnetic forces. that's, those forces are the reason for their being mixed into condensed (liquid or stable) states. In those condensed states, the movement of the debris relative to each other proceeds in orderly type; their person houses in addition to the electrical and magnetic dipole moments and the radiation and absorption spectra, in most cases range little through comparability with their houses within the unfastened nation. Exceptiotls are the exact so-called collective states of condensed media which are shaped lower than part transitions of the second one sort. The collective states of subject are characterised to a excessive measure through the micro-ordering that arises due to the interplay among the debris and that's damaged down by way of chaotic thermal movement less than heating. Examples of such pheonomena are the superfluidity of liquid helium, and the superconductivity and ferromagnetism of metals, which exist in basic terms at temperatures less than the severe temperature. At low temperature states the debris don't express their person features and behavior themselves as a unmarried complete in lots of respects. They stream alongside capillaries in ordered style and create an undamped present in a conductor or a macroscopic magnetic second. during this regard the cloth acquires specific homes that aren't frequently inherent to it.
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Extra info for Collective Effects in Quantum Statistics of Radiation and Matter
K c. It is natural to call k c the correlation momentum since for k - k c there occurs a transition from the free-particle spectrum to the linear phonon spectrum. As is well known, the linear branch of the excitations is responsible for the cubic dependence of the heat capacity on the temperature; thus we achieve a qualitative agreement between the theoretical description and the experimental data that we recalled in the preamble to this section. Note that when A = 0, the expressions that we have obtained for the Green's functions and the energy spectrum in the normal and superfluid states transfer from one to the other.
The expressions for the total functions are not known in advance, so that a system of equations is set up in order (0 determine them. 48) which represents it as the sum of an infinite number of diagrams of the skeleton diagram technique, the elements of which are the total Green's functions. The skeleton diagram technique proves to be useful, in particular, in theories with anomalous Green's functions, 1 which are identically zero in calculations according to the standard perturbation theory. 2).
It is well known that the total Green's function G(p) can be expressed in terms of the irreducible self-energy part l:(p), which is the sum of the contributions of all the diagrams with two legs such that the entry of the diagram cannot be separated from the exit by cutting one line of the diagram. The partial summation of diagrams allowing one to express the function G (p) in terms of G o(p ) and L(p) is clear from the graph equation .. - '-"'---;®~"----I@~"'+ + + ------i@. 46) The analytic form of this equation is G(p) = Go(p) + Go(p) :I:(p) Go(p) + Go(p):I:(p)Go(p) x x :I:(p )Go(p) + ...
Collective Effects in Quantum Statistics of Radiation and Matter by V. N. Popov, V. S. Yarunin (auth.)