Ground states of large bosonic systems: The gross Pitaevskii limit revisited

Nam P, Rougerie N, Seiringer R. 2016. Ground states of large bosonic systems: The gross Pitaevskii limit revisited. Analysis and PDE. 9(2), 459–485.


Journal Article | Published | English

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Abstract
We study the ground state of a dilute Bose gas in a scaling limit where the Gross-Pitaevskii functional emerges. This is a repulsive nonlinear Schrödinger functional whose quartic term is proportional to the scattering length of the interparticle interaction potential. We propose a new derivation of this limit problem, with a method that bypasses some of the technical difficulties that previous derivations had to face. The new method is based on a combination of Dyson\'s lemma, the quantum de Finetti theorem and a second moment estimate for ground states of the effective Dyson Hamiltonian. It applies equally well to the case where magnetic fields or rotation are present.
Publishing Year
Date Published
2016-03-24
Journal Title
Analysis and PDE
Volume
9
Issue
2
Page
459 - 485
IST-REx-ID

Cite this

Nam P, Rougerie N, Seiringer R. Ground states of large bosonic systems: The gross Pitaevskii limit revisited. Analysis and PDE. 2016;9(2):459-485. doi:10.2140/apde.2016.9.459
Nam, P., Rougerie, N., & Seiringer, R. (2016). Ground states of large bosonic systems: The gross Pitaevskii limit revisited. Analysis and PDE. Mathematical Sciences Publishers. https://doi.org/10.2140/apde.2016.9.459
Nam, Phan, Nicolas Rougerie, and Robert Seiringer. “Ground States of Large Bosonic Systems: The Gross Pitaevskii Limit Revisited.” Analysis and PDE. Mathematical Sciences Publishers, 2016. https://doi.org/10.2140/apde.2016.9.459.
P. Nam, N. Rougerie, and R. Seiringer, “Ground states of large bosonic systems: The gross Pitaevskii limit revisited,” Analysis and PDE, vol. 9, no. 2. Mathematical Sciences Publishers, pp. 459–485, 2016.
Nam P, Rougerie N, Seiringer R. 2016. Ground states of large bosonic systems: The gross Pitaevskii limit revisited. Analysis and PDE. 9(2), 459–485.
Nam, Phan, et al. “Ground States of Large Bosonic Systems: The Gross Pitaevskii Limit Revisited.” Analysis and PDE, vol. 9, no. 2, Mathematical Sciences Publishers, 2016, pp. 459–85, doi:10.2140/apde.2016.9.459.
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