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Pair Excitations and the Mean Field Approximation of Interacting Bosons, I

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Abstract

In our previous work (Grillakis et al. in Commun Math Phys 294:273–301, 2010; Adv Math 228:1788–1815, 2011) we introduced a correction to the mean field approximation of interacting Bosons. This correction describes the evolution of pairs of particles that leave the condensate and subsequently evolve on a background formed by the condensate. In Grillakis et al. (Adv Math 228:1788–1815, 2011) we carried out the analysis assuming that the interactions are independent of the number of particles N. Here we consider the case of stronger interactions. We offer a new transparent derivation for the evolution of pair excitations. Indeed, we obtain a pair of linear equations describing their evolution. Furthermore, we obtain a priori estimates independent of the number of particles and use these to compare the exact with the approximate dynamics.

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  1. University of Maryland, College Park, MD, USA

    M. Grillakis & M. Machedon

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  1. M. Grillakis
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  2. M. Machedon
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Correspondence to M. Machedon.

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Communicated by H.-T. Yau

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Grillakis, M., Machedon, M. Pair Excitations and the Mean Field Approximation of Interacting Bosons, I. Commun. Math. Phys. 324, 601–636 (2013). https://doi.org/10.1007/s00220-013-1818-7

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  • DOI: https://doi.org/10.1007/s00220-013-1818-7

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