Chapter 18 BoseEinstein Gases (Part II)
18.2 BoseEinstein 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 blackbody 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 BE 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 BoseEinstein 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 BE statistics.
We consider an ideal boson gas consisting of N particles in a volume V. The BE
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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 Winter '10
 Dr.asdas
 mechanics, Photon, Radiation, Trigraph, tc, ground state, Boson

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