Can Mean Particle Numbers Be Negative in BEC Transition?

[pivoxa15]

Homework Statement

So the transition temperture is defined when at a given temperture the mean number of particles in the lowest state is 0. So does that imply there are tempertures where the mean value is a negative number?

The Attempt at a Solution

If not than surely at 1000k, the mean number in the lowest state is still 0 so there is no unique transition temperture. However this problem is overcome by setting T=0 which would mean the number of particles in the ground state must increase. So when it is 0, it will be the start of the occupation of the ground state as it can only increase because we have set T=0 in order to calculate the zeta function.

 

[Jhero]

You are correct in your understanding that the transition temperature is defined as the temperature at which the mean number of particles in the lowest state is 0. This means that at this temperature, the system undergoes a transition from a state where the ground state is unoccupied to a state where it becomes occupied.

To answer your question, it is not possible for the mean number of particles in the lowest state to be a negative number. This is because the mean number of particles is a measure of the average number of particles in a given state, and it cannot be a negative value. If it were negative, it would imply that there are "negative particles" in the system, which is not physically possible.

Furthermore, at temperatures above the transition temperature, there will still be a mean number of 0 particles in the lowest state. This does not mean that there is no unique transition temperature. The transition temperature is still defined as the temperature at which the mean number of particles in the lowest state becomes non-zero.

In regards to your statement about setting T=0, it is important to note that this is a theoretical concept used in calculations to simplify the zeta function. In reality, there is no such thing as absolute zero temperature, and the ground state will always have some non-zero occupation at any temperature above absolute zero.

I hope this helps clarify your understanding of the concept of transition temperature. Please let me know if you have any further questions. Keep up the good thinking and curiosity!