物理课件27-2.pptVIP

27.3 Bose-Einstein distribution Photon gas Satyendra Nath Bose (1894–1974) Indian physicist. In 1924 he mailed paper titled Planck Law and Light Quantum Hypothesis to Einstein. Soon afterwards Einstein published two papers Quantum Theory of Monatomic Ideal Gases Einstein translated it from English to German himself, after attaching a translator’s note on 1924 July second mailed to Berlin Zeitschrift fur Physik for publication. Ehrenfest Uhlenbeck ‘Only small math error’ 27.3 Bose-Einstein distribution Photon gas For quantal ideal Bose gases, Particles obey of Bose-Einstein distribution: m ? 0, E = 0: ?n? ? ? ( fBE ≥ 0 ) It is related to the fact that number of photons is not conserved. Blackbody radiation ~ photon gas (s = 1) It is Bose distribution with m = 0. Planck distribution: For phonon gas we have m = 0 too, but DOS is different. Ultraviolet Catastrophe an oscillator in equilibrium with radiation High frequency oscillators are more probable to lose energy and keep a relatively lower energy. High frequency divergence is restrained. Rayleigh-Jeans law leads to ultraviolet catas-trophe. Planck: Stefan-Boltzmann law Let , we have density of energy *27.4 Bose-Einstein condensation T = T0, m = 0 T ? T0 ? Bose-Einstein condensation (BEC) Bose-Einstein condensate Where do the particles condense to? k = 0 state in k space in real space more ordered more disordered BEC free expansion C is continuous Phase transition of third order! In July 1995 a group in Boulder Colorado headed by C. Wieman and E. Cornell cloud of 87Rb atoms,170nk. In July a group of Rice University led by R. G. Hulet in system of 7Li atoms , 17nK In October, W. Ketterle of MIT and coworkers a system of Na atoms, 2mK. rapid cooling high production rate of condensed atoms to take data about 30 times faster 300 times more BEC than Colorado group Cornell