Lecture 36: Fermi and Bose particlesLecture 36: Fermi and Bose particlesChapter 10, Friday April 11Chapter 10, Friday April 11thth• The Fermi gas at T = 0• Properties of a Fermi gas as T → 0• Examples of Fermi systemsReading: Reading: All of chapter 10 (pages 188 All of chapter 10 (pages 188 --207)207)Homework 10 due Wed. Apr. 16th at 5pmHomework 10 due Wed. Apr. 16th at 5pmAssigned problems, Assigned problems, Ch. 10Ch. 10::Exam 3 next Friday (18th), Exam 3 next Friday (18th), ChsChs88--1010Review next week (time/place TBA)Review next week (time/place TBA)Fermi/Bose distribution functionsFermi/Bose distribution functions()()() /() /1()11()1BBFkkTBkkTnkefkeεμεμ−−=+=−()/BkTεμ−knFermi/Bose distribution functionsFermi/Bose distribution functions()()() /() /1()11()1BBFkkTBkkTnkefkeεμεμ−−=+=−kn()/BkTεμ−n ~ nQnQ~ T3/2FermiFermi--Dirac distribution functionDirac distribution function0.00 0.25 0.50 0.75 1.00 1.25 1.500.00.20.40.60.81.01.2n(k)ε(k)/εF εF/kBT T = 0 50 20 10()() /1()1BkkTnkeεμ−=+0123-4-20−T lnTTemperatureTT--dependence of chemical potentialdependence of chemical potentialClassicalkkyykkxxkkzzFermi surfaceFermi surface()1/323Fknπ=2/32328Fhnmεπ⎛⎞=⎜⎟⎝⎠/FFBTkε=3535FFNUuεε==FermiFermi--Dirac distribution functionDirac distribution function0.00 0.25 0.50 0.75 1.00 1.25 1.500.00.20.40.60.81.01.21.4n(k)ε(k)/εFεF/kBT = 50()() /1()1BkkTnkeεμ−=+dndε−FFTTαε⎛⎞⎜⎟⎝⎠LowLow--temperature heat capacitytemperature heat capacity22el BFTCNkTπ=3el latlatCC CCT=+∝CopperLowLow--temperature contribution to entropytemperature contribution to entropyLinear regimeExamples of Fermi systemsExamples of Fermi systemsDilute 3He in superfluid 4HeExamples of Fermi systemsExamples of Fermi systemsElectrons in metals (dense
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