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Unformatted text preview: C es = T dS es dT , (5) where S es is the entropy of the Bogoliubons and is given by the standard result for a collection of ±ermions: S = − 2 k B s k [(1 − f k ) ln (1 − f k ) + f k lnf k ] . (6) 1 Here f k = 1 e βE k + 1 (7) and E k = r Δ 2 + ξ 2 k , (8) Δ being the energy gap, which we assume is real, and ξ k = ǫ k − E F . Show that the specifc heat can be written as C es = 2 βk B s k p − ∂f k ∂E k Pp E 2 k + 1 2 β d Δ 2 dβ P , (9) where β = 1 / ( k B T ). Show explicitly that, iF Δ is temperatureindependent, the specifc heat varies at low temperatures as exp( − Δ /k B T ) multiplied by a Function which varies more slowly with temperature. (This is also true even iF Δ is dependent on temperature, provided that it remains fnite at T = 0.) 2...
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 Fall '10
 STROUD
 Physics, Thermodynamics, Entropy, Heat, Fundamental physics concepts

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