Bose Einstein Condensation. In Diluted Gas. Condensed Matter II –Spring 2007 Davi Ortega. Summary. From counting to a new state of matter Indistinguishability of particles Counting indistinguishable particles Einstein’s conclusion = New State Some properties
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Bose Einstein Condensation
In Diluted Gas
Condensed Matter II –Spring 2007
Average number of occupation
for each energy state
Cannot occupy the same level
Can occupy the same level
Particle in a 3D box:
Calculating explicitly the total number:
But what happens now if I let at this temperature the density n V of the substance increase(e.g., by isothermal compression) to even higher values?
I claim that in this case a number of molecules which always grows with the total density makes a transition to the 1. quantum state (state without kinetic energy)… … The claim thus asserts that something similar happens as when isothermally compressing a vapor beyond the volume of saturation. A separation occurs; a part “condenses”, the rest remains a “saturated ideal gas”. (Einstein, 1925).
The order of the de Broglie wavelenght is the same as the volume ocupied by the ensemble
Number of the particles that falls to the “condensate” state
This whole theory assume non interacting particles: Schrödinger Equation
Interacting Particles: Gross-Pitaeviski Eq.
All Optical BEC