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A Brief Introduction to Bose-Einstein Condensation

A Brief Introduction to Bose-Einstein Condensation. 國立彰化師範大學物理系 郭西川 (July 29, 2003, NCTS). gas. solid. Phases of matter. liquid. The fifth phase?. BEC. The coldest and the most fragile matter ever found in the universe. plasma.

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A Brief Introduction to Bose-Einstein Condensation

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  1. A Brief Introduction to Bose-Einstein Condensation 國立彰化師範大學物理系 郭西川 (July 29, 2003, NCTS)

  2. gas solid Phases of matter liquid The fifth phase? BEC The coldest and the most fragile matter ever found in the universe plasma

  3. The shape of the radiation spectrum of an ideal black–body (Planck, 1900)

  4. For any given temperature T, a black-body absorb all the thermal radiation incident upon its surface and emit thermal radiation with the same spectrum at the same temperature. An ideal black-body can be modeled by a cavity inside a body connected by a small hole to the outside. Thus the problem of black-body radiation is equivalent to the problem ofthermal radiation in a cavity.

  5. discrete energy packet (quantum) equi-partition of energy among cavity modes

  6. Bose-Einstein statistics (1924-1925) In 1924, S.N. Bose rederived the Planck formula by considering the cavity radiation as an ideal photon gas. The photons are indistinguishable so that the exchange of two photons in one energy cell (see the following figure) does not lead to a new state.

  7. Einstein generalized Bose statistics to the systems containing fixed number of atoms and claimed the existence of a macroscopically occupied ground state (the so-called Bose-Einstein condensation.) Schematic diagram of the Bose-Einstein distribution for a system of particles at a temperature T.

  8. Some remarks on BEC (homogeneous) 1. condensation in momentum space 2. occurs even in the absence of inter-particle interactions 3. phase coherence of the condensate (broken U(1) symmetry) 4. critical phase-space density: 5. no BEC in 1-D and 2-D

  9. 自旋1/2 自旋角動量(spin angular momentum)

  10. Spin-statistics Theorem All particles with integer spin are bosons (玻色子), and all particles with half-integer spin are fermions (費米子). field quantum:photon, pion, graviton, gluon,... bosons composite boson:4He, 23Na, 87Rb,... Total Spin = Nucleon Spin + Electron Spin All atoms with an even number of neutrons are bosons 75% of the atoms in the periodic table are bosons

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