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Abstract
We provide explicit lower bounds for the groundstate energy of the renormalized Nelson model in terms of the coupling constant α and the number of particles N, uniform in the meson mass and valid even in the massless case. In particular, for any number of particles N and large enough α, we provide a bound of the form Cα^{2}N^{3} log^{2}(αN), where C is an explicit positive numerical constant; and if α is sufficiently small, we give one of the form Cα^{2}N^{3} log^{2} N for N ≥ 2 and Cα^{2} for N = 1. Whereas it is known that the renormalized Hamiltonian of the Nelson model is bounded below (as realized by Nelson) and implicit lower bounds have been given elsewhere (as in a recent work by Gubinelli, Hiroshima, and Lörinczi), ours seem to be the first fully explicit lower bounds with a reasonable dependence on α and N. We emphasize that the logarithmic term in the bounds above is probably an artifact in our calculations since one would expect that the groundstate energy should behave as Cα^{2}N^{3} for large N or α, as in the polaron model of Fröhlich.
Originalsprog  Engelsk 

Artikelnummer  061901 
Tidsskrift  Journal of Mathematical Physics 
Vol/bind  59 
Nummer  6 
ISSN  00222488 
DOI  
Status  Udgivet  1 jun. 2018 
Fingeraftryk
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 1 Afsluttet

Semiclassical Quantum Mechanics
Fournais, S. (PI), Madsen, P. (Deltager), Mikkelsen, S. (Deltager), Miqueu, J.P. C. (Deltager) & Bley, G. (Deltager)
01/07/2015 → 31/12/2020
Projekter: Projekt › Forskning