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

By Michael V. Sadovskll

The creation of quantum box conception equipment has resulted in one of those “revolution” in condensed subject thought. This led to the elevated value of Feynman diagrams or diagram strategy. It has now develop into crucial for execs in condensed topic conception to have a radical wisdom of this technique. there are lots of solid books that conceal the final elements of diagrammatic equipment. while, there was a emerging desire for books that describe calculations and methodical “know how” of particular difficulties for rookies in graduate and postgraduate classes. This precise selection of lectures addresses this want. the purpose of those lectures is to illustrate the applying of the diagram strategy to diverse difficulties of condensed topic conception. a few of these difficulties are usually not “finally” solved. however the improvement of effects from any element of this booklet might function a place to begin for a major theoretical examine.

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1999)]. In case of randomly placed magnetic impurities in non magnetic metal, Eq. L. (1989)]. 5 Electron self-energy, effective mass and damping of quasiparticles Our final aim is to calculate single-particle Green's function in a system with Coulomb (or also some other) interaction. g. via some partial summation of diagram series. What physical information can be obtained in this way? We know that the Green's function of free electrons Go(pe) has a pole at ep = ^ — fi. 46) Electron-Electron Interaction 29 where e p represents the spectrum of "renormalized" quasiparticles.

11) defines full polarization of the systems. Similarly we can obtain RPA expression for magnetic susceptibility. In this case we have to analyze the response of a system to infinitesimal magnetic field, flipping electronic spin. Dropping technical details, we just note that here it is sufficient to consider diagrams shown in Fig. I. V. (2003)]. e. 13) 22 Diagrammatics O + CD Fig. 6 Diagrams for magnetic susceptibility. ± denote spin projections. I. 15) where us is the Bohr magneton and g is so called g-factor (for free electrons 3 = 2).

Let us estimate the contribution to the imaginary part of E from the process of creation of three quasiparticles (see Fig. 11) — the simplest process leading to the finite lifetime of a quasiparticle. g. e. to the creation of an electron-hole pair. Volovik, 1991). 9 We shall deal mostly with the case of spin s = 1/2. t Fig. 122) Now it is clear that for the case of |pi| —> pp, for all the other excitations we also have |p2|, \ps\, |p4| —> pf, while for z\ —> +0 leads also to eQ(ct = 2,3,4) —> 0.

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