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Fluctuations of a Bose-Einstein condensate at
finite temperatures Mariusz Gajda Instytut
Fizyki PAN WMP UKSW BEC in Poland Torun
18.05-19.05 2007
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Statistical Ensambles
isolated system
Microcanonical partition function
reservoir
Canonical partition function
system
E
Grand canonical partition function
reservoir
system
N E
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Bose-Einstein condensation of the ideal gas in a
harmonic trap
3D isotropic harmonic trap
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Bose-Einstein condensation of the ideal gas in a
harmonic trap
Two characteristic energy scales
Macroscopic occupation of the ground state
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Relative population of a condensate
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Grand Canonical functions catastrophe
Unphysical result!!!
Below Tc the ground state contribution dominates
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Microcanonical Ensamble
Partition function is equal to a
number of microstates of N-particle system of
total energy E
Econst. Nconst.
Hard to calculate anything!
Ramanujan (1918) partition of integer nn1...nk
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Maxwll Deamon Ensamble
approximation
excited subsystem
reservoir
P. Navez, D. Bitouk, M. Gajda, Z. Idziaszek, K.
Rzazewski, PRL 79, 1789, (1997)
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Microcanonical Fluctuations
excited system
N
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Canonical Fluctuations of Condensate
excited system
N
E
energy reservoir
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Asymptotic analitic formulas
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(No Transcript)
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Measure condensate fraction many timesfor each
temperature Plot error bars Publish PRL