MIT OpenCourseWarehttp://ocw.mit.edu 8.512 Theory of Solids II Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.� � 1 8.512 Theory of Solids II Problem Set 6 Due March 31, 2008 1. The response function Kµνdefined by Jµ= −KµνAνcan be decomposed into the transverse and longitudinal parts. Kµν(q, ω) = δµν−qµqq2 νK⊥(q, ω) + qµqq2 νKk(q, ω) (a) Starting from the linear response expression, calculate K⊥(q, ω= 0) for a free Fermi gas. [It may be useful to choose q = qzˆ and compute Kxx.] (b) Using the results from (a), show that the Landau diamagnetic susceptibility (in-cluding spin degeneracy) is given by e2kFχD= −12π2mc2 Check that this is −1/3 of the Pauli spin susceptibility. For an alternative deriva-tion using Landau levels, please study the discussion in Landau and Lifshitz’s Statistical Physics, Vol. 1,
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