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  
PPZ_22.pdf

accesso aperto

Tipologia: Published (publisher's version)
Licenza: Creative commons
Dimensione 493.34 kB
Formato Adobe PDF
493.34 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3410656
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
  • OpenAlex ND
social impact