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Displaying similar documents to “Classical KMS Condition and Tomita-Takesaki Theory”

On Woronowicz's approach to the Tomita-Takesaki theory

László Zsidó (2012)

Banach Center Publications

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The Tomita-Takesaki Theory is very complex and can be contemplated from different points of view. In the decade 1970-1980 several approaches to it appeared, each one seeking to attain more transparency. One of them was the paper of S. L. Woronowicz "Operator systems and their application to the Tomita-Takesaki theory" that appeared in 1979. Woronowicz's approach allows a particularly precise insight into the nature of the Tomita-Takesaki Theory and in this paper we present a brief, but...

On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation

François Castella (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We present the semi-conductor Boltzmann equation, which is time-reversible, and indicate that it can be formally derived by considering the large time and small perturbing potential limit in the Von-Neumann equation (time-reversible). We then rigorously compute the corresponding asymptotics in the case of the Von-Neumann equation on the Torus. We show that the limiting equation we obtain does not coincide with the physically realistic model. The former is indeed an equation of Boltzmann...