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 warm-up, 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 particle-hole 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 (quasi-particles)? 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
- Electron, Fundamental physics concepts, Condensed matter physics, Lindhard function