Unformatted text preview: tial V local ( r ) = U Â· Î´ ( r ) (2) shows a diï¬€erent behaviour at q = 0. In this exercise we basically follow the sections (3.2.1) and (3.2.2) of the lecture notes. a) As a warmup, derive the relation between the particle distribution Î´n ( r ,t ) and its induced potential V ind ( r ,t ) in the ( k ,Ï‰ )space. b) Find the imaginary part of the response function Ï‡ ( q ,Ï‰ ) for small q â€™s. What is the dispersion relation in the lowest order in q ? c) The upper boundary line of the particlehole continuum is given by Ï‰ q, max = ~ 2 m ( q 2 + 2 k F q ) = ~ q 2 2 m + v F q, (3) where v F is the Fermi velocity and q =  q  . What is the condition on U for stable plasmon excitations (quasiparticles)? Oï¬ƒce hour: Monday, April 4th, 2011  9:00 to 11:00 am HIT K 31.3 Tama Ma...
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 Spring '11
 Sigrist
 Electron, Fundamental physics concepts, Condensed matter physics, Lindhard function

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