Mean-field analysis of Bose–Einstein condensation in general power-law potentials

2004 ◽  
Vol 37 (12) ◽  
pp. 2593-2605 ◽  
Author(s):  
O Zobay
Keyword(s):  
Power Law ◽  
Mean Field ◽  
Field Analysis ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
General Power ◽  
Bose Einstein

scholarly journals Strong Kac’s chaos in the mean-field Bose–Einstein Condensation

2019 ◽  
Vol 20 (05) ◽  
pp. 2050031
Author(s):  
Sergio Albeverio ◽  
Francesco C. De Vecchi ◽  
Andrea Romano ◽  
Stefania Ugolini
Keyword(s):  
Scaling Limit ◽  
Mean Field ◽  
Stochastic Approach ◽  
Fixed Time ◽  
Path Space ◽  
Einstein Condensation ◽  
Mean Field Limit ◽  
Bose Einstein Condensation ◽  
Bose Einstein ◽  
Energy Convergence

A stochastic approach to the (generic) mean-field limit in Bose–Einstein Condensation is described and the convergence of the ground-state energy as well as of its components are established. For the one-particle process on the path space, a total variation convergence result is proved. A strong form of Kac’s chaos on path-space for the [Formula: see text]-particles probability measures is derived from the previous energy convergence by purely probabilistic techniques notably using a simple chain-rule of the relative entropy. Fisher’s information chaos of the fixed-time marginal probability density under the generic mean-field scaling limit and the related entropy chaos result are also deduced.

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