Disintegration of KMS-states and reduction of standard von Neumann algebras

Riedel, Norbert

doi:10.2140/pjm.1984.111.415

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…This set K( * ∞ 1 A, * ∞ 1 σ) is a compact affine set in the weak * -topology and is known to be a Choquet simplex whose extreme points are those φ ∈ K( * ∞ 1 A, * ∞ 1 σ), the von Neumann algebras generated by images of whose GNS-representations are factors (cf. [5], [9] and [11]).…”

Section: The Simplex Of Kms Quantum Symmetric Statesmentioning

confidence: 99%

KMS quantum symmetric states

Dykema

Mukherjee

2017

Journal of Mathematical Physics

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Let $A$ be a unital C$^*$-algebra and let $\sigma$ be a one-parameter automorphism group of $A$. We consider $\operatorname{QSS}_\sigma(A)$, the set of all quantum symmetric states on $*_1^\infty A$ that are also KMS states (for a fixed inverse temperature, for specificity taken to be $-1$) for the free product automorphism group $*_1^\infty\sigma$. We characterize the elements of $\operatorname{QSS}_\sigma(A)$, we show that $\operatorname{QSS}_\sigma(A)$ is a Choquet simplex whenever it is nonempty and we characterize its extreme points.Comment: 14 page

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Section: The Simplex Of Kms Quantum Symmetric Statesmentioning

confidence: 99%

KMS quantum symmetric states

Dykema

Mukherjee

2017

Journal of Mathematical Physics

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“…However, it is of interest to prove the following conjecture for the general non separable situation. The reader is also referred to [15] for some connected results.…”

Section: On the Reduction Theorymentioning

confidence: 99%

An Ergodic Theorem for Quantum Diagonal Measures

Fidaleo

2009

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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We extend the Nonconventional Ergodic Theorem for generic measures by Furstenberg, to several situations of interest arising from quantum dynamical systems. We deal with the diagonal state canonically associated to the product state (i.e. quantum "diagonal measures"), or to convex combinations of diagonal measures for non ergodic cases. For the sake of completeness, we treat also the Nonconventional Ergodic Theorem for compact dynamical systems, that is when the unitary generating the dynamics in the GNS representation is almost periodic. The Nonconventional Ergodic Theorem allows in a natural way to determine the limit of the three-point correlations, naturally relevant for the knowledge of the ergodic properties of a dynamical system. Mathematics Subject Classification: 46L55, 47A35, 37A55.

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“…The PMP is then transformed into a probable maximum flood (PMF) hydrograph after deduction of losses and determination of antecedent properties, such as soil moisture content (Pilgrim and Cordery 1993). The application of PMP to estimate the PMF has become a standard for dam design in some countries where no risk of overtopping can be approved: e.g., the USA (e.g., Riedel 1976;USNWS 1978;Hansen 1987), Canada (e.g., Gagnon et al 1970), China (e.g., Wang 1987Pan andTeng 1988), India (e.g., CWC 1972;Rakhecha et al 1990), and Australia (e.g., Kennedy 1982). Hence, the importance of maximum precipitable water vapor or potential water vapor (POWV) in an area is revealed.…”

Section: Introductionmentioning

confidence: 99%

An Analytical Formula for Potential Water Vapor in an Atmosphere of Constant Lapse Rate

Varmaghani¹

2012

Terr. Atmos. Ocean. Sci.

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Accurate calculation of precipitable water vapor (PWV) in the atmosphere has always been a matter of importance for meteorologists. Potential water vapor (POWV) or maximum precipitable water vapor can be an appropriate base for estimation of probable maximum precipitation (PMP) in an area, leading to probable maximum flood (PMF) and flash flood management systems. PWV and POWV have miscellaneously been estimated by means of either discrete solutions such as tables, diagrams or empirical methods; however, there is no analytical formula for POWV even in a particular atmospherical condition. In this article, fundamental governing equations required for analytical calculation of POWV are first introduced. Then, it will be shown that this POWV calculation relies on a Riemann integral solution over a range of altitude whose integrand is merely a function of altitude. The solution of the integral gives rise to a series function which is bypassed by approximation of saturation vapor pressure in the range of -55 to 55 degrees Celsius, and an analytical formula for POWV in an atmosphere of constant lapse rate is proposed. In order to evaluate the accuracy of the suggested equation, exact calculations of saturated adiabatic lapse rate (SALR) at different surface temperatures were performed. The formula was compared with both the diagrams from the US Weather Bureau and SALR. The results demonstrated unquestionable capability of analytical solutions and also equivalent functions.

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Disintegration of KMS-states and reduction of standard von Neumann algebras

Cited by 4 publications

References 15 publications

KMS quantum symmetric states

KMS quantum symmetric states

An Ergodic Theorem for Quantum Diagonal Measures

An Analytical Formula for Potential Water Vapor in an Atmosphere of Constant Lapse Rate

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