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Graduate Lecture Series 29 June – 3 July, 2009 Prof Ngee-Pong Chang

Graduate Lecture Series 29 June – 3 July, 2009 Prof Ngee-Pong Chang. Lecture 3 Bose Gas & Bose-Einstein Condensate. Bose – Einstein Statistics 1924. 1894 - 1974. 1879 - 1955. Bose letter to Einstein June 4, 1924. SN Bose, Zeit f Phys v26, 178 (1924); v27, 384 (1924).

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Graduate Lecture Series 29 June – 3 July, 2009 Prof Ngee-Pong Chang

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  1. Graduate Lecture Series 29 June – 3 July, 2009 Prof Ngee-Pong Chang Lecture 3 Bose Gas & Bose-Einstein Condensate

  2. Bose – Einstein Statistics 1924 1894 - 1974 1879 - 1955

  3. Bose letter to Einstein June 4, 1924 SN Bose, Zeit f Phys v26, 178 (1924); v27, 384 (1924) The Historical Development of Quantum Theory, Jagdish Mehra and Helmut Rechenberg, p569 (2001); Writings on physics and philosophy by W Pauli, Charles Paul Enz, K. vMeyenn, R. Schlapp, p. 94 (citation of Bose papers)

  4. Inclusive vs Exclusive

  5. Bosons in a Box Standing Wave Eigenfunction L L L

  6. At T > 0 Probability of Occupancy

  7. Probability of Occupancy Classical limit Fermion Boson Large E

  8. Bose-Einstein Distribution for spin-0 bosons or fugacity E=0 Positive octant

  9. Bose-Einstein Condensate

  10. Bose-Einstein Distribution for spin-0 bosons fugacity or

  11. Riemann Zeta function

  12. varies monotically from z = 0 to z = 1 For small z At high temperatures

  13. l A T i i t t c r c a c Critical Temperature

  14. Crude estimate of Tc for He4 You can check that this gives a Tc value of 3.17 K, to be compared with the experimentally observed value of 2.18 K

  15. J.C. Davies group (Cornell) http://www.iranika.ir/articles%20page/mohandesi/mechanic.superfluids1.htm

  16. Bose-Einstein Condensate Term The number of zero energy bosons per unit volume

  17. University of Stuttgart measurement of BEC of Chromium atoms http://www.pi5.uni-stuttgart.de/news/050303/news050303.html

  18. Bose-Einstein Condensate 400 nK 200 nK 50 nK

  19. Nobel Prize in Physics 2001

  20. Cornell – Wieman experiment: Cooling two thousand Rubidium-87 atoms to below 170 nK using combination of laser cooling and magnetic evaporative cooling. Ketterle (MIT) experiment Cooled some hundred times more atoms (Na23) , and was able to demonstrate quantum mechanical interference between two BEC.

  21. Magnetic Evaporative Cooling

  22. For a visual applet on Magnetic Evaporative Cooling Go to http://www.colorado.edu/physics/2000/atomic_lab.html

  23. For a visual applet on Laser Cooling of Atoms Go to http://www.colorado.edu/physics/2000/atomic_lab.html

  24. Ketterle experiment http://online.itp.ucsb.edu/plecture/ketterle/oh/45.html

  25. Nobel Prize in Physics 1997

  26. Transition Temperature Douglas Osheroff 1945 -

  27. Nobel Prize in Physics 1997

  28. 2 Polarization states Photon Gas Photon energy N is a function of temperature At equilibrium, fugacity, z, rises to maximum value of 1

  29. Pressure By comparing with the equation for U, we find that the pressure-energy relation for the photon gas is

  30. Or

  31. ( ) ( = ) k k 2 + ! ! ¼ n a = Phonon Gas http://ocw.mit.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-730Physics-for-Solid-State-ApplicationsSpring2003/8A2B76D2-7D99-445B-B511-EDFA06C0482B/0/lecture12c.pdf

  32. Speed of sound in solid

  33. Peter Debye 1884 – 1966 Verh. Deut. Phys. Ges. 15, 678-689 (1913)

  34. Low Temperature Limit

  35. Low Temperature Limit Specific Heat of Solid at low temperature

  36. High Temperature Limit Dulong Petit Law

  37. http://web.mit.edu/6.730/www/ST04/Lectures/Lecture12.pdf

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