Why is z=1 below Tc in Bose Einstein condensation?

In summary, at temperatures below the critical temperature (Tc), the particles in a Bose Einstein condensate (BEC) all occupy the same quantum state, resulting in a macroscopically observable state known as Bose Einstein condensation. The parameter z=1 below Tc indicates that the system has undergone a phase transition to a BEC, where the particles behave as a single entity due to their quantum behavior. A value of z=1 below Tc is the critical value that indicates the presence of a BEC and affects its properties such as superfluidity and coherence. The value of z remains at 1 below Tc and any additional particles added to the system will also occupy the same state, maintaining the coherence of the
  • #1
eas123
9
0
Hi.

For a Bose gas, my textbook states that below the critical temperature, which is given by n(λth)3/(2S+1)=2.612, the fugacity z=eβμ≈1.

Why is this? The most basic explanation possible would be ideal, as I only need the rough idea.

Thanks! :smile:
 
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  • #2
Or chemical potential μ=0, i.e. the energy of the ground state. Would it be lower, not even the ground state would be populated. Would it be higher, the population of the ground state would be infinite.
 

1. Why is z=1 below Tc in Bose Einstein condensation?

At temperatures below the critical temperature (Tc), the particles in a Bose Einstein condensate (BEC) exhibit quantum behavior and all occupy the same quantum state. This results in a macroscopically observable state known as Bose Einstein condensation, where the particles behave as a single coherent entity. The parameter z represents the number of particles in the lowest energy state, and at Tc, z=1 because all particles are in the same state. Below Tc, z remains at 1 as the particles continue to occupy the same state, resulting in the characteristic behavior of a BEC.

2. How does z=1 below Tc relate to the transition to a Bose Einstein condensate?

The parameter z=1 below Tc indicates that the system has undergone a phase transition to a Bose Einstein condensate. This means that the particles in the system are now in a state of maximum coherence and behave as a single entity, rather than individual particles. This phenomenon is a result of the quantum behavior of the particles and is a hallmark of Bose Einstein condensation.

3. Is there a specific value of z that indicates the presence of a Bose Einstein condensate?

Yes, a value of z=1 indicates the presence of a Bose Einstein condensate. This value is known as the critical value and is directly related to the critical temperature (Tc) of the system. At Tc and below, z=1 represents the maximum coherence of the particles in a BEC.

4. How does the value of z=1 below Tc affect the properties of a Bose Einstein condensate?

The value of z=1 below Tc is directly related to the properties of a Bose Einstein condensate. This value indicates that all particles in the system are in the same quantum state and behave as a single entity. As a result, the BEC exhibits properties such as superfluidity, where the particles can flow without resistance, and coherence, where the particles exhibit correlated behavior on a macroscopic scale.

5. Can the value of z change below Tc in a Bose Einstein condensate?

No, the value of z remains at 1 below Tc in a Bose Einstein condensate. This is because the particles have already reached maximum coherence and occupy the same quantum state. Any additional particles added to the system will also occupy the same state, maintaining the value of z=1. However, the number of particles in the system can change, resulting in the expansion or contraction of the BEC, but the value of z will remain at 1.

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