| Autor: |
Grillakis, Manoussos G., Machedon, Matei, Margetis, Dionisios |
| Rok vydání: |
2009 |
| Předmět: |
|
| Zdroj: |
Communications in Mathematical Physics, 294, 273-301 (2010) |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1007/s00220-009-0933-y |
| Popis: |
Inspired by the works of Rodnianski and Schlein and Wu, we derive a new nonlinear Schr\"odinger equation that describes a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a many-particle system in Bose-Einstein condensation. We show that our new equation, if it has solutions with appropriate smoothness and decay properties, implies a new Fock space estimate. We also show that for an interaction potential $v(x)= \epsilon \chi(x) |x|^{-1}$, where $\epsilon$ is sufficiently small and $\chi \in C_0^{\infty}$, our program can be easily implemented locally in time. We leave global in time issues, more singular potentials and sophisticated estimates for a subsequent part (part II) of this paper. |
| Databáze: |
arXiv |
| Externí odkaz: |
|
