Derivation of Effective Evolution Equations from Many Body Quantum Dynamics
Abstract
We review some recent results concerning the derivation of effective evolution equations from first principle quantum dynamics. In particular, we discuss the derivation of the Hartree equation for mean field systems and the derivation of the Gross-Pitaevskii equation for the time evolution of Bose-Einstein condensates.
- Publication:
-
XVITH INTERNATIONAL CONGRESS ON MATHEMATICAL PHYSICS. Held 3-8 August 2009 in Prague
- Pub Date:
- March 2010
- DOI:
- arXiv:
- arXiv:0910.3969
- Bibcode:
- 2010maph.conf..406S
- Keywords:
-
- Mean field systems;
- Hartree equation;
- Bose-Einstein condensates;
- Gross-Pitaevskii equation;
- Mathematical Physics;
- 81U05;
- 81U30;
- 81V70;
- 82C10
- E-Print:
- 9 pages. Contribution to the Proceedings of the International Congress on Mathematical Physics held in Prague in August 2009