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Communications in Mathematical Physics

, Volume 136, Issue 3, pp 625–632 | Cite as

Continuity and relative hamiltonians

  • Matthew J. Donald
Article

Abstract

Let (ω n ) n ≧1 be a norm convergent sequence of normal states on a von Neumann algebraA withω n ω. Let (k n ) n≧1 be a strongly convergent sequence of self-adjoint elements ofA withk n k. It is shown that the sequence\((\omega _n^{k_n } )_{n \geqq 1} \) of perturbed states converges in norm toω ω . A related result holds forC*-algebras. A counter-example is provided to show that it is not sufficient to assume weak convergence of (ω n ) n ≧1 even whenkn=k for alln. However, conditions are given which, together with weak convergence, are sufficient. Relative entropy methods are used, and a relative entropy inequality is proved.

Keywords

Entropy Neural Network Statistical Physic Normal State Complex System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Matthew J. Donald
    • 1
  1. 1.The Cavendish LaboratoryCambridgeUK

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