The quantum information manifold for epsilon-bounded forms

Details The quantum information manifold for epsilon-bounded forms The quantum information manifold for epsilon-bounded forms

1999-10-19

arxiv.org/abs/math-ph/9910031v1

Reports on Mathematical Physics, Vol. 46 (2000), 325-335.

Physics

Mathematical Physics

12 pages, report to Torun Conference, 1999

Scientific paper

10.1016/S0034-4877(00)90003-X

Let H be a self-adjoint operator bounded below by 1, and let V be a small form perturbation such that RVS has finite norm, where R is the resolvent at zero to the power 1/2 +epsilon, and S is the resolvent to the power 1/2-epsilon. Here, epsilon lies between 0 and 1/2. If the Gibbs state defined by H is sufficiently regular, we show that the free energy is an analytic function of V in the sense of Frechet, and that the family of density operators defined in this way is an analytic manifold modelled on a Banach space.

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