mean field asymptotics
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scholarly journals A weak KAM approach to the periodic stationary Hartree equation

2021 ◽  
Vol 28 (6) ◽  
Author(s):  
L. Zanelli ◽  
F. Mandreoli ◽  
F. Cardin
Keyword(s):  
Ground State ◽  
Kam Theory ◽  
Mean Field ◽  
Hartree Equation ◽  
Many Body ◽  
Semiclassical Asymptotics ◽  
The Mean ◽  
Mean Field Asymptotics ◽  
Periodic Setting ◽  
Integral Identities

AbstractWe present, through weak KAM theory, an investigation of the stationary Hartree equation in the periodic setting. More in details, we study the Mean Field asymptotics of quantum many body operators thanks to various integral identities providing the energy of the ground state and the minimum value of the Hartree functional. Finally, the ground state of the multiple-well case is studied in the semiclassical asymptotics thanks to the Agmon metric.

scholarly journals Quantum mean-field asymptotics and multiscale analysis

2019 ◽  
Vol 1 (2) ◽  
pp. 221-272 ◽  
Author(s):  
Zied Ammari ◽  
Sébastien Breteaux ◽  
Francis Nier
Keyword(s):  
Multiscale Analysis ◽  
Mean Field ◽  
Mean Field Asymptotics
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