Bose-Einstein condensate

  • #1
MathematicalPhysicist
Gold Member
4,289
203

Main Question or Discussion Point

In the book A Quantum Approach to Condensed Matter Physics by Taylor and Heinonen they write the following passage on page 87:

Thus there is a temperature ##T_c##, defined by ##N_0(T_c)=N##, below which the zero-energy state is occupied by a macroscopic number of particles. This phenomenon is known as the Bose-Einstein condensation, and is remarkable in being a phase transition that occurs in the absence of inter-particle forces.
Now I don't understand what does it mean "macroscopic number", how many particles?
 

Answers and Replies

  • #2
DrDu
Science Advisor
6,032
759
It means that ##N/N_0 = O(N_0^0)## if N is the number of particles in the condensate and ##N_0## the total number of particles, or, easier, ##N =O(N_0)##.
 
Last edited:
  • #3
MathematicalPhysicist
Gold Member
4,289
203
@DrDu the total number of particles in where? (in the universe, just outside the condensate, it's not clear to me).

So obviously, ##N=aN_0## where ##0<a<1##.
 
  • #4
DrDu
Science Advisor
6,032
759
First, I don't know whether my use of ##N## and ##N_0## coincides with the one from your book.
I consider ##N_0## to be the number of all particles in the substance you are considering while ##N## is the number of particles in the "condensate", i.e. the number of particles in the ground state, or, more generally if the particles are interacting, the lowest eigenvalue of the 1-density matrix.
 
  • #5
674
131
It just means a significant number of the particles in the system are in the groundstate, say half of them.
 
  • Like
Likes Spinnor
  • #6
1
2
In the book A Quantum Approach to Condensed Matter Physics by Taylor and Heinonen they write the following passage on page 87:



Now I don't understand what does it mean "macroscopic number", how many particles?
The mathematical definition of a macroscopical number of particles is that the ratio Number of particles N to the volume V of the system remains finite as V goes to infinity i.e. the density of particles is finite in the thermodynamic limit.
 
  • #9
DrClaude
Mentor
7,339
3,521
2 is enough or we need ##\infty##?
:cool:
How many grands of sand do you need to make a pile?

Condensates can easily be made with 106-107 atoms.
 

Related Threads on Bose-Einstein condensate

  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
10
Views
5K
  • Last Post
Replies
11
Views
5K
  • Last Post
Replies
3
Views
932
  • Last Post
Replies
2
Views
662
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
8
Views
27K
Replies
1
Views
2K
Top