Effective non-linear dynamics of binary condensates and open problems. (English) Zbl 1374.81103
Michelangeli, Alessandro (ed.) et al., Advances in quantum mechanics. Contemporary trends and open problems. Cham: Springer (ISBN 978-3-319-58903-9/hbk; 978-3-319-58904-6/ebook). Springer INdAM Series 18, 239-256 (2017).
Summary: We report on a recent result concerning the effective dynamics for a mixture of Bose-Einstein condensates, a class of systems much studied in physics and receiving a large amount of attention in the recent literature in mathematical physics; for such models, the effective dynamics is described by a coupled system of nonlinear Schödinger equations. After reviewing and commenting our proof in the mean-field regime from a previous paper, we collect the main details needed to obtain the rigorous derivation of the effective dynamics in the Gross-Pitaevskii scaling limit.
For the entire collection see [Zbl 1378.81009].
For the entire collection see [Zbl 1378.81009].
MSC:
| 81V70 | Many-body theory; quantum Hall effect |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 82C26 | Dynamic and nonequilibrium phase transitions (general) in statistical mechanics |
| 35G50 | Systems of nonlinear higher-order PDEs |
