Can you give me a simple explanation of my question about BEC (Bose Einstein Condensate)
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Can you give me a simple explanation of my question about BEC (Bose Einstein Condensate)

[From: ] [author: ] [Date: 12-05-27] [Hit: ]
the balls spread out and become less defined. Eventually a point is reached when their fuzziness(where they are positioned) overlaps. At this time atoms lose their individual identities. They all have the same quantum state and coalesce into a single super atom .The properties of condensates are quite bizarre. These include,......
What is it made of, how do they make it, and what state of matter is is in?

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At temperatures approaching absolute zero, the atoms in a gas are in their lowest energy level. At these temperatures quantum mechanical effects become more apparent.
As a result of their probability positioning, atoms can be thought of as fuzzy balls. When the temperature decreases, the balls spread out and become less defined. Eventually a point is reached when their fuzziness(where they are positioned) overlaps.
At this time atoms lose their individual identities. They all have the same quantum state and coalesce into a single 'super atom' .The properties of condensates are quite bizarre. These include, increased optical density(enough to slow photons down to walking speed!) and
super fluidity(absence of viscosity). BEC classify as, naturally, a low-temperature state of matter which contains super fluids, Fermionic condensates, Rydberg molecules, quantum Hall states and the quark-type matter aptly named 'strange' matter.

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A Bose Einstein condensate is made up of particles with integer spin. These particles are called bosons an example of bosons is the helium atom that has spin zero. There is a lot of other particles with integer spins. Particles that have half integer spins are called fermions and obey an other statistics called Fermi-Dirac.

bosons obey the statistical distribution called Bose distribution:

P(E) = B/{e^[(a*kT+E)/kT] -1}

B is some normalization constant

Where P(E) is the probability of a particles to be in an ensemble at an energy E, K is the Boltzmann constant, "e" is the euler's number, T is the absolute temperature and "a" is a parameter sometimes called chemical potential. We can think of "a" as the energy increment ( or decrement ) in a system when we introduce a new particle in it.

If ther is a minimum energy level E0 different of zero for the particles in the system, as is the case of particles closed into a box, then, we can have:

e^(a*kT+E0)/kT -1 = 0

e^(a*kT+E0)/kT =1

a*kT+E0 = 0

T = -E0/(a*k)

then, P(E0) goes to infinite for the energy E0.

If "a" is negative, there is a positive temperature T given by the above equation that makes P(E0) = infinite.

This means that at this temperature all particles go to the level E0 and they all share the same wave function corresponding to that energy level. There is no more microscopic individual wave functions but only one macroscopic wave function shared by all particles. The ensemble behaves in very bizarre ways as is the case for liquid helium at temperatures around 2.7K. It loses its viscosity and becomes a perfect inviscid fluid. That means it flows in a steady state for an infinite time with no frictional internal forces appearing as far as the temperature is not raised.
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