Diagrammatics: lectures on selected problems in condensed by Michael V. Sadovskll

By Michael V. Sadovskll

The creation of quantum box concept equipment has ended in a type of “revolution” in condensed subject thought. This ended in the elevated significance of Feynman diagrams or diagram procedure. It has now turn into principal for execs in condensed subject thought to have an intensive wisdom of this technique. there are lots of sturdy books that conceal the overall points of diagrammatic equipment. even as, there was a emerging desire for books that describe calculations and methodical “know how” of particular difficulties for newcomers in graduate and postgraduate classes. This exact selection of lectures addresses this want. the purpose of those lectures is to illustrate the appliance of the diagram strategy to various difficulties of condensed topic thought. a few of these difficulties are usually not “finally” solved. however the improvement of effects from any part of this e-book might function a place to begin for a major theoretical research.

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For T > 0 we have to use Matsubara technique. 79)) Matsubara formalism is useless, as it deals with imaginary time r . However, as we shall see now, Matsubara technique allows rather simple approach to calculation of the linear response. E. (1963)]: • Analytic continuation of XAB (wm) fr°m t n e discrete set of points at positive imaginary half-axis of frequency w = iujn (n > 0) to the real axis (Imu> —> +0) precisely gives us the retarded susceptibility XAB(V)This theorem allows us to determine XAB(W) using XAB (wrn) calculated using Matsubara diagram technique.

12. ). In fact, the existence of discontinuity in particle distribution allows strict definition of the Fermi surface in the system of interacting Fermions. 130) has a typical form of a smeared quasiparticle without interactions Fermiliquid rika z kF Fig. 12 k Qualitative form of particle distribution function in the Fermi-liquid at T = 0. -'-(^-^ Fig. 13 Spectral density in Fermi-gas (a) and in Fermi-liquid (b). (Lorentzian) peak at e = ep (quasiparticle energy), on the smooth background due to multi-particle excitations, as shown in Fig.

It should be clearly understood that the ground state of a normal Fermi-liquid is not the only possible ground state of the system of interacting Fermions. For example we know, that the system may be in the superconducting (superfluid) state, when Luttinger theorem does not apply and there is no Fermi surface in the usual sense — it is "closed" by the energy gap. Presently, much attention is being paid to strongly correlated electronic systems with many "scenarios" of the formation of non Fermi-liquid state.

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