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Unformatted text preview: tial V local ( r ) = U · δ ( r ) (2) shows a diﬀerent 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 δn ( r ,t ) and its induced potential V ind ( r ,t ) in the ( k ,ω )-space. b) Find the imaginary part of the response function χ ( q ,ω ) for small q ’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 ω 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)? Oﬃce hour: Monday, April 4th, 2011 - 9:00 to 11:00 am HIT K 31.3 Tama Ma...
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This note was uploaded on 10/04/2011 for the course PHYS fs11 taught by Professor Sigrist during the Spring '11 term at Swiss Federal Institute of Technology Zurich.
- Spring '11