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Chapter 18 (IV)

# Chapter 18 (IV) - Chapter 18 Bose-Einstein Gases(Part II...

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Chapter 18 Bose-Einstein Gases (Part II) 18.2 Bose-Einstein Condensation 18.2.1 Introduction In 1924, S. N. Bose sent to Einstein a paper, in which Planck formula was derived by entirely statistical argument, treating black-body radiation as a photon gas. This is in the content of 18.1. Einstein realized the importance of the paper and helped Bose publish it in Z. für Physik. Moreover, Einstein immediately started to work on the problem by himself, and publish two papers in 1924 and 1925, developing the full picture of quantum theory of bosonic particles. The concept of particles obeying B-E statistics was born, and today we know that all entities with an integer spin will display the total symmetry characterizing this statistics. Einstein noted that if the number of particles N is conserved, even totally noninteracting particles will undergo a phase transition at low enough temperatures. This transition is termed Bose-Einstein condensation (BEC), which was predicted by Einstein in 1925. Bose did not find this feature because he was discussing photons which have zero rest mass do not need to condense, because they can disappear instead, when the energy of the system is decreased. 18.2.2. BEC As discussed in Chapter 13, bosons are particles of integer spin that obey B-E statistics. We consider an ideal boson gas consisting of N particles in a volume V. The B-E distribution function is given by 1 1 / ) ( = = kT j j j j e g N f μ ε or 1 1 ) ( ) ( ) ( / ) ( = = kT e g N f μ ε ε ε ε . (18.27) For a given temperature, there is only one parameter in f j or f( ε ), that is, the chemical potential μ . Thus, we have to get the chemical potential μ (T) in order to get f( ε ).

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Chapter 18 (IV) - Chapter 18 Bose-Einstein Gases(Part II...

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