# Bose-Einstein condensate

Gold Member

## 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?

Related Atomic and Condensed Matter News on Phys.org
DrDu
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:
Gold Member
@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##.

DrDu
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.

It just means a significant number of the particles in the system are in the groundstate, say half of them.

• Spinnor
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.

Demystifier
Gold Member
Now I don't understand what does it mean "macroscopic number", how many particles?
##\gg 1##

Gold Member
##\gg 1##
2 is enough or we need ##\infty##? DrClaude
Mentor
2 is enough or we need ##\infty##? How many grands of sand do you need to make a pile?

Condensates can easily be made with 106-107 atoms.

Gold Member
How many grands of sand do you need to make a pile?
one.

Demystifier
• 