A Bose-Einstein condensate

MathematicalPhysicist

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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?
 

DrDu

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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)##.
 
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MathematicalPhysicist

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@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

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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.
 

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