The quantum information manifold for ε-bounded forms

Let H 0 ≥ I be a self-adjoint operator and let V be a form-small perturbation such that ▪, where ϵ ϵ (0, 1 2 ) and R 0 = H −1 0. Suppose that there exists a positive β < 1 such that Z 0 ≔ Tr e −β H 0 < ∞. Let Z ≔ Tr e −( H 0+ V) . Then we show that the free energy Ψ = log Z is an analytic func...

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Bibliographic Details
Published in:Reports on mathematical physics 2000-12, Vol.46 (3), p.325-335
Main Authors: Grasselli, M.R., Streater, R.F.
Format: Article
Language:English
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Summary:Let H 0 ≥ I be a self-adjoint operator and let V be a form-small perturbation such that ▪, where ϵ ϵ (0, 1 2 ) and R 0 = H −1 0. Suppose that there exists a positive β < 1 such that Z 0 ≔ Tr e −β H 0 < ∞. Let Z ≔ Tr e −( H 0+ V) . Then we show that the free energy Ψ = log Z is an analytic function of V in the sense of Fréchet, and that the family of density operators defined in this way is an analytic manifold.
ISSN:0034-4877
1879-0674
DOI:10.1016/S0034-4877(00)90003-X