Operator Algebras and Quantum Statistical Mechanics

Bratteli, Ola; Robinson, Derek W.

doi:10.1007/978-3-662-09089-3

Cited by 721 publications

(862 citation statements)

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“…To my disappointment I hardly got anything. Assuming nobody else has tried recently, the present knowledge on these flows does not seem to exceed much what is already presented in Bratteli-Robinson's book [2,3] and Sakai's book [15]; notable results there are concerned with KMS states and representations in addition to a broad theory of unbounded derivations and generators and a theory in AF algebras.…”

Section: Introductionmentioning

confidence: 81%

Lifting of an Asymptotically Inner Flow for a Separable C*-Algebra

Kishimoto

2006

Operator Algebras

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Section: Introductionmentioning

confidence: 81%

Lifting of an Asymptotically Inner Flow for a Separable C*-Algebra

Kishimoto

2006

Operator Algebras

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“…The mathematical structure of the fluctuation algebra is discussed in many places in the literature, see e.g. [GVV1]- [GVV6] and [MSTV,BR2,Pe,OP,De2] for general results about CCR algebras. For notational and reference purposes we recall a few basic facts.…”

Section: Theorem 14mentioning

confidence: 99%

“…They are part of a wider program initiated in [Ru2,Ru3,JP1,JP2,JP4] which deals with the development of a mathematical theory of non-equilibrium statistical mechanics in the framework of algebraic quantum statistical mechanics [BR1,BR2,Pi]. For additional information about this program we refer the reader to the reviews [Ru4,JP3,AJPP1].…”

Section: Introductionmentioning

confidence: 99%

Central Limit Theorem for Locally Interacting Fermi Gas

Jakšić

Pautrat

Pillet

2008

Commun. Math. Phys.

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We consider a locally interacting Fermi gas in its natural non-equilibrium steady state and prove the Quantum Central Limit Theorem (QCLT) for a large class of observables. A special case of our results concerns finitely many free Fermi gas reservoirs coupled by local interactions. The QCLT for flux observables, together with the Green-Kubo formulas and the Onsager reciprocity relations previously established [JOP4], complete the proof of the Fluctuation-Dissipation Theorem and the development of linear response theory for this class of models.

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“…As an intermediate step of independent interest, we will consider a variant of these spaces, using the Fermions and Clifford algebras. The necessary background on these topics can be found in [4,20].…”

Section: Spinorial Subspacesmentioning

confidence: 99%

Completely 1-complemented subspaces of Schatten spaces

Merdy

Ricard

Roydor

2008

Trans. Amer. Math. Soc.

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Abstract. We consider the Schatten spaces S p in the framework of operator space theory and for any 1 ≤ p = 2 < ∞, we characterize the completely 1-complemented subspaces of S p . They turn out to be the direct sums of spaces of the form S p (H, K), where H, K are Hilbert spaces. This result is related to some previous work of Arazy and Friedman giving a description of all 1-complemented subspaces of S p in terms of the Cartan factors of types 1-4. We use operator space structures on these Cartan factors regarded as subspaces of appropriate noncommutative L p -spaces. Also we show that for any n ≥ 2, there is a triple isomorphism on some Cartan factor of type 4 and of dimension 2n which is not completely isometric, and we investigate L p -versions of such isomorphisms.

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Operator Algebras and Quantum Statistical Mechanics

Cited by 721 publications

References 0 publications

Lifting of an Asymptotically Inner Flow for a Separable C*-Algebra

Lifting of an Asymptotically Inner Flow for a Separable C*-Algebra

Central Limit Theorem for Locally Interacting Fermi Gas

Completely 1-complemented subspaces of Schatten spaces

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