Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Lecture 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 - 207)All of chapter 10 (pages 188 - 207)Homework 10 due Wed. Apr. 16th at Homework 10 due Wed. Apr. 16th at 5pm5pmAssigned problems, Assigned problems, Ch. 10Ch. 10::Exam 3 next Friday (18th), Chs 8-10Exam 3 next Friday (18th), Chs 8-10Review next week (time/place TBA)Review next week (time/place TBA)Fermi/Bose distribution functionsFermi/Bose distribution functions( )( )( ) /( ) /1( )11( )1BBFk k TBk k Tn kef kee me m--=+=-( )/Bk Te m-knFermi/Bose distribution functionsFermi/Bose distribution functions( )( )( ) /( ) /1( )11( )1BBFk k TBk k Tn kef kee me m--=+=-kn( )/Bk Te m-n ~ nQnQ ~ T 3/2Fermi-Dirac distribution functionFermi-Dirac distribution function0.00 0.25 0.50 0.75 1.00 1.25 1.500.00.20.40.60.81.01.2n(k)(k)/F F/kBT T = 0 50 20 10( )( ) /1( )1Bk k Tn kee m-=+0 1 2 3-4-20 T lnTTemperatureTT-dependence of chemical potential-dependence of chemical potentialClassicalkkyykkxxkkzzFermi surfaceFermi surface( )1/ 323Fk np=2 / 3232 8Fh nmep� �=� �� �/F F BT ke=3535FFNUuee==Fermi-Dirac distribution functionFermi-Dirac distribution function0.00 0.25 0.50 0.75 1.00 1.25 1.500.00.20.40.60.81.01.21.4n(k)(k)/FF/kBT = 50( )( ) /1( )1Bk k Tn kee m-=+dnde-FFTTa e� �� �� �Low-temperature heat capacityLow-temperature heat capacity22el BFTC NkTp=3el latlatC C CC T= +�CopperLow-temperature contribution to entropyLow-temperature 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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