Bose-Einstein Condensate Properties

[bob012345]

I don't know what you calculated there, but this has nothing to do with the HUP. The extent of the spatial wave function of each atom depends on the size of the trap (think "particle in a box," with all atoms in the ground state).Electrons are fermions, so I don't see how they could all occupy the same state by themselves. It is the atom as a whole that is a boson and the atoms in the BE-condensed phase are all in the same state. Your interpretation is incorrect.

I'm probably wrong. But all I did was to calculate delta x delta p >=hbar/2 I got a thermal velocity from the temperature and p from that and the mass of Rubidium. The conduction bands in metals and semiconductors are one state. But the nuclei of the supporting atoms are in a fixed grid where each atom is localized, not smeared out. The nuclei can be considered classical otherwise Molecular Mechanics would not work for complex molecules but it does.

 

[DrClaude]

I'm probably wrong. But all I did was to calculate delta x delta p >=hbar/2 I got a thermal velocity from the temperature and p from that and the mass of Rubidium.

The atoms in the BEC are not in a thermal state. That's why it is a different state of matter with a phase transition. Your calculation is meaningless. You have to calculate the ground state of the trapping potential.

The conduction bands in metals and semiconductors are one state.

It is not one state but, as the name says, a band of states.

But the nuclei of the supporting atoms are in a fixed grid where each atom is localized, not smeared out. The nuclei can be considered classical otherwise Molecular Mechanics would not work for complex molecules but it does.

Things are different in a solid. And I wouldn't say that the nuclei are classical in molecules, but they are localized (and MM is based on many approximations).

 

[bob012345]

The atoms in the BEC are not in a thermal state. That's why it is a different state of matter with a phase transition. Your calculation is meaningless. You have to calculate the ground state of the trapping potential.It is not one state but, as the name says, a band of states.Things are different in a solid. And I wouldn't say that the nuclei are classical in molecules, but they are localized (and MM is based on many approximations).

Thanks. How does one correctly apply the HUP to a BEC then? Or does it just not apply? Regarding the classical limit in molecular calculations, I assume the HUP can give an estimate.

 

[DrClaude]

Thanks. How does one correctly apply the HUP to a BEC then? Or does it just not apply? Regarding the classical limit in molecular calculations, I assume the HUP can give an estimate.

The HUP applies to simultaneous measurement of two quantities. It is not relevant for the discussion of the BEC, where the atoms are in a well defined energy state, with the Hamiltonian being the kinetic energy + trapping potential.

In the classical limit, both position and momentum have definite values, which is not the case in QM because of the HUP. There is indeed a link there.

 

[bob012345]

The HUP applies to simultaneous measurement of two quantities. It is not relevant for the discussion of the BEC, where the atoms are in a well defined energy state, with the Hamiltonian being the kinetic energy + trapping potential.

In the classical limit, both position and momentum have definite values, which is not the case in QM because of the HUP. There is indeed a link there.

Thanks. That brings up the concept of what do we mean by 'measurement'. I believe every interaction between everything in nature constitutes a 'measurement' and thus obeys the HUP at all times and situations. Thus every Rb atom in the BEC obeys the HUP at continuously. I assume you disagree? I never thought the HUP was principally about humans taking data.

 

[DrClaude]

Thanks. That brings up the concept of what do we mean by 'measurement'. I believe every interaction between everything in nature constitutes a 'measurement' and thus obeys the HUP at all times and situation. Thus every Rb atom in the BEC obeys the HUP at continuously. I assume you disagree? I never thought the HUP was principle about humans taking data.

This is getting off-topic.

But no, all interaction is not a measurement, especially not a particular type of measurement. Take the example of spin. If a prepare system in the spin-up state according to the z axis, it is in an undetermined spin state along x and y. If something interacts with that spin in a way that can't change the spin, by your account its spin would become indeterminate with respect to all axes. I expect it to stay in the spin-up state along z.

Anyway, you will find a few recent threads on the question of the HUP and its meaning. Please have a look at them.

 

[bob012345]

This is getting off-topic.

But no, all interaction is not a measurement, especially not a particular type of measurement. Take the example of spin. If a prepare system in the spin-up state according to the z axis, it is in an undetermined spin state along x and y. If something interacts with that spin in a way that can't change the spin, by your account its spin would become indeterminate with respect to all axes. I expect it to stay in the spin-up state along z.

Anyway, you will find a few recent threads on the question of the HUP and its meaning. Please have a look at them.

Thanks, I will.