By V. N. Popov, V. S. Yarunin (auth.)

Material debris, electrons, atoms, molecules, engage with each other by way of electromagnetic forces. that's, those forces are the reason for their being mixed into condensed (liquid or strong) states. In those condensed states, the movement of the debris relative to each other proceeds in orderly model; their person houses in addition to the electrical and magnetic dipole moments and the radiation and absorption spectra, as a rule range little by means of comparability with their houses within the unfastened country. Exceptiotls are the specific so-called collective states of condensed media which are shaped lower than section transitions of the second one style. The collective states of subject are characterised to a excessive measure via the micro-ordering that arises as a result of interplay among the debris and that's damaged down through chaotic thermal movement lower than heating. Examples of such pheonomena are the superfluidity of liquid helium, and the superconductivity and ferromagnetism of metals, which exist merely at temperatures lower than the serious temperature. At low temperature states the debris don't convey their person features and behavior themselves as a unmarried complete in lots of respects. They move alongside capillaries in ordered style and create an undamped present in a conductor or a macroscopic magnetic second. during this regard the fabric acquires distinct homes that aren't frequently inherent to it.

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**Additional resources for Collective Effects in Quantum Statistics of Radiation and Matter**

**Sample text**

19) B(p) .. taPo. 15) we obtain the non-trivial solution for Po = lexl2 : 2toPo+2toP1-toPO-J,1 = 0, whence Po = 1:. - 2p1 = 1:. 20) where A = J,1- 2t o(41t)-3f2 C(3/2) T3I2. 20) that a positive solution for the density Po of the condensate exists only for A > O. 21 ) gives in first approximation the equation of the phase transition line in the J,1- T-plane. For A> 0 we have a superfluid state and for A < 0, a normal state. 20) we obtain the formula for the total density: P = Po +P1 = io -(41t)-3f2 C(3/2) T3I2.

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) + ... = Go(p) + Go(p ):I:(p )G(p). l. 47) 28 CHAPTER 1 Thus in calculating the Green's function G(p), it suffices to find its selfenergy part. We now consider the modification of perturbation theory called the skeleton diagram technique.

0- a = + --0-- + -<:x:>-- + .. c:x:>2 + ... 1For the rest of this section we use a system of units with 2m - 1, where m is the mass of the Bose particle. 44 CHAPTER 2 c -®-=t+p+f::>c>+· .. Fig. 17) The main contribution to the sum over the internal momenta is carried here by k - a -1 » T1/2» Jl1/2. We can therefore ignore Jl in the unperturbed Green's function and replace the sum over the frequencies in this equation by an integral. 17) can be represented in the form In what follows we shall be conSidering this function in the region k « a- 1, Olc< 8:2.