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

ISBN-10: 9400929838

ISBN-13: 9789400929838

ISBN-10: 9401078408

ISBN-13: 9789401078405

Material debris, electrons, atoms, molecules, have interaction 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 style; their person houses in addition to the electrical and magnetic dipole moments and the radiation and absorption spectra, in general differ little via comparability with their houses within the unfastened country. Exceptiotls are the precise so-called collective states of condensed media which are shaped less than section transitions of the second one variety. The collective states of subject are characterised to a excessive measure by way of the micro-ordering that arises due to the interplay among the debris and that is 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 under the severe temperature. At low temperature states the debris don't show their person features and behavior themselves as a unmarried complete in lots of respects. They stream alongside capillaries in ordered model and create an undamped present in a conductor or a macroscopic magnetic second. during this regard the cloth acquires exact houses that aren't frequently inherent to it.

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**Sample text**

The above operator method of examination is not directly applicable at non-zero temperatures. A more general theory will be constructed later using the temperature Green's functions in the functional-integral representation. In conclusion we note the important fact that the symmetry of the original Hamiltonian H with respect to the gradient transformation R = e iaN, N = L~"'k' [H,R] =0 is not enjoyed by the approximating Hamiltonian: k [H,R]::F- O. The absence of gradient invariants for the Hamiltonian H leads to a violation of the selection rules for the equilibrium thermodynamical averages.

23) corresponding to the correction (41t)-1 T(2A)1/2 to the density: ~p = = (121t)-1 T(2A)3/2. The corresponding correction to the pressure for the normal state is equal to (61t)-1 TIAI3I2_ SUPERFLUIDITY To conclude this section we consider the phenomenon of superfluidity. We take a Bose system in a system of coordinates moving with velocity v _ In this case. the system is described by the action functional SUPERFLUID BOSE SYSTEMS s ~ + j J d 'r d 3X 2~ v(V'I'*'I' - 49 '1'. 39). 31 ) which means that the system moves as a whole with velocity v.

34) with boundary conditions: '1'(0) = z', 'I'*(~) = z*. The solutions of these equations have the form 'l'o(t) = z'e- rot - {e-ro(t-t')j(t')dt" o 'l'ott) .. z*ero(t-P) +fero(t-t')j*(t')dt'. p The value of the phase at the extremal is given by FUNCTIONAL INTEGRALS IN QUANTUM THEORY <1>10 = - Jr"'odt + o z*"'o(~) = = z'z*e-~ - z*f Pe-ro(P-1')j(t')dt' o + f p 1 fPj",~dt +z"l'~(O) =- 0 and we obtain the formula ZJPe-ro1j*(t')dt' + 0 rdtf e- ro (1-1')j(t')dt' o 19 0 JO'l"'O",e41 = e 4l0 for the functional integral.

### Collective Effects in Quantum Statistics of Radiation and Matter by V. N. Popov, V. S. Yarunin (auth.)

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