We prove that the flow of the discrete nonlinear Schrödinger equation (DNLS) is the mean field limit of the quantum dynamics of the Bose–Hubbard model for N interacting particles. In particular, we show that the Wick symbol of the annihilation operators evolved in the Heisenberg picture converges, as N becomes large, to the solution of the DNLS. A quantitative Lp-estimate, for any p≥ 1 , is obtained with a linear dependence on time due to a Gaussian measure on initial data coherent states.
Mean Field Derivation of DNLS from the Bose–Hubbard Model
Picari E.;Ponno A.;Zanelli L.
2022
Abstract
We prove that the flow of the discrete nonlinear Schrödinger equation (DNLS) is the mean field limit of the quantum dynamics of the Bose–Hubbard model for N interacting particles. In particular, we show that the Wick symbol of the annihilation operators evolved in the Heisenberg picture converges, as N becomes large, to the solution of the DNLS. A quantitative Lp-estimate, for any p≥ 1 , is obtained with a linear dependence on time due to a Gaussian measure on initial data coherent states.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
Picari2021_Article_MeanFieldDerivationOfDNLSFromT.pdf
accesso aperto
Tipologia:
Published (publisher's version)
Licenza:
Creative commons
Dimensione
505.76 kB
Formato
Adobe PDF
|
505.76 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
