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Characterization of states of infinite boson systems

I. On the construction of states of boson systems

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Abstract

In a previous paper [11] it was shown that to each locally normal state of a boson system one can associate a point process that can be interpreted as the position distribution of the state. In the present paper the so-called conditional reduced density matrix of a normal or locally normal state is introduced. The whole state is determined completely by its position distribution and this function. There are given sufficient conditions on a point processQ and a functionk ensuring the existence of a state such thatQ is its position distribution andk its conditional reduced density matrix. Several examples will show that these conditions represent effective and useful criteria to construct locally normal states of boson systems. Especially, we will sketch an approach to equilibrium states of infinite boson systems. Further, we consider a class of operators on the Fock space representing certain combinations of position measurements and local measurements (observables related to bounded areas). The corresponding expectations can be expressed by the position distribution and the conditional reduced density matrix. This class serves as an important tool for the construction of states of (finite and infinite) boson systems. Especially, operators of second quantization, creation and annihilation operators are of this type. So, independently of the applications in the above context this class of operators may be of some interest.

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Authors and Affiliations

  1. Mathematische Fakultät, Friedrich-Schiller-Universität Jena, UHH 17.06, O-6900, Jena, Federal Republic of Germany

    Karl-Heinz Fichtner & Wolfgang Freudenberg

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  1. Karl-Heinz Fichtner
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  2. Wolfgang Freudenberg
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Communicated by Ya. G. Sinai

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Fichtner, KH., Freudenberg, W. Characterization of states of infinite boson systems. Commun.Math. Phys. 137, 315–357 (1991). https://doi.org/10.1007/BF02431883

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  • DOI: https://doi.org/10.1007/BF02431883

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