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Gibbs measures based on 1d (an)harmonic oscillators as mean-field limits

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NAM Phan Thanh LEWIN Mathieu ROUGERIE Nicolas

Rok publikování 2018
Druh Článek v odborném periodiku
Časopis / Zdroj Journal of Mathematical Physics
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
Doi http://dx.doi.org/10.1063/1.5026963
Klíčová slova Nonlinear Schrodinger-equation; reduced density-matrices; quantum continuous systems; global well-posedness; invariant-measures; thermodynamic limit; correlation inequalities; classical limit; gases property
Popis We prove that Gibbs measures based on 1D defocusing nonlinear Schrodinger functionals with sub-harmonic trapping can be obtained as the mean-field/large temperature limit of the corresponding grand-canonical ensemble for many bosons. The limit measure is supported on Sobolev spaces of negative regularity, and the corresponding density matrices are not trace-class. The general proof strategy is that of a previous paper of ours, but we have to complement it with Hilbert-Schmidt estimates on reduced density matrices. Published by AIP Publishing.

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