Nonlocal mean-field theory in N-body quantum mechanics for Bose-Einstein condensation

2002 ◽  
Author(s):  
Bernard Deconinck ◽  
J. Nathan Kutz
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Mean Field Theory ◽  
Mean Field ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Bose Einstein

Lattice Quantum Mechanics: An Application to Bose–Einstein Condensation

1998 ◽  
Vol 09 (08) ◽  
pp. 1577-1585 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Quantum Mechanics ◽  
Kinetic Theory ◽  
Specific Form ◽  
Einstein Condensation ◽  
Nonrelativistic Quantum ◽  
Bose Einstein Condensation ◽  
Formal Analogy ◽  
Lattice Quantum ◽  
Nonrelativistic Quantum Mechanics ◽  
Bose Einstein

A lattice formulation of nonrelativistic quantum mechanics is presented, based on a formal analogy with discrete kinetic theory. The method is applied to the Gross–Pitaevski equation, a specific form of self-interacting nonlinear Schrödinger equation relevant to the study of Bose–Einstein condensation.

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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