nhóm 4 ngưng tụ khí bose

7.4 Bose Condensation
Bose gas is particle systems have characteristics:
• Homogeneous particle systems: the system has
photon particles, the medon, atoms have even
electrons...these particles are Bose particles.
• Spin whole or zero.
• Interdependence between particles can be ignored.


7.4 Bose Condensation
•7.4.1
  Apply Bose-Einstein distribution to calculate the
total number of particles
- Consider an energy interval :
Suppose that in the interval d� has dN the energy level.
The number of particles in the range of d is:
d
dn(�) = dN (7.1)
( : the mean number of particles on an energy level)


7.4 Bose Condensation
-•  Bose-Einstein distribution:
(non-degenerate)
According to theoretical mechanics: the number of
standing wave has a modulus of wave vector within +
d:
dN( (7.2)


7.4 Bose Condensation

We have :
On the orther hand :
=>
So

put in (7.2):
 (7.3)


7.4 Bose Condensation
In quantum statistics, the particle state depends on have
g=2s+1 spin orientation
There are g possible states where the degenerate
level of ℇ is g = 2s + 1
(7.4)


7.4 Bose Condensation
- Particles with energy in the range 

dn( (7.5)
The total number of particles of the system is N,so
N= (7.6)
 From

this equation can identify some characteristics of
Bose gas


7.4 Bose Condensation

7.4.2 Chemical potential properties
a) Chemical potential <0:
Number of particles dn()>0 (7.5) then <0
=> (-1) >0 => >1 with all values .
b) � decreases when T is increased
Put U( (7.7)


7.4 Bose Condensation
• We
  have:

= ==•We have then >0 then
•Then � decreases when T is increased


7.4 Bose Condensation
7.4.3 Bose condensation phenomenon
 Since μ is inversely proportional to T, when T
decreases, μ increases (μ <0) so μ →0 at a
certain temperature.
 When θ== k then µ= 0
 Temperature is called degenerate temperature(
or


7.4 Bose Condensation
When T , change và µ= 0 to calculate the total
number of particles of the system
(7.8)

7.4 Bose Condensation
Putting : I = and
.
→ I = có

→ (7.9)
→Degenerate temperature
(7.10)


7.4 Bose Condensation
When 0 < T < then µ= 0 and called the number of
particles at temperature θ is N’
→ (7.11)
(7.9) and (7.11) →
→


7.4 Bose Condensation
 
• Generality:
But the total number of particles of the system is
unchanged, it is thought that at temperature T< the
number of particles ΔN = N –N’ is not in the fraction
BE transferred to the lowest energy level (or “energy
level zero”).
The so-called Bose condensation phenomenon.