KMS States and Conformal Measures

Kms States and the Chemical Potential for Disordered Systems

We extend the theory of the chemical potential associated to a compact separable gauge group to the case of disordered quantum systems. This is done in the natural framework of operator algebras. Among the other results, we show that the chemical potential does not depend on the disorder. The situation of the n–torus is treated in some detail. Indeed, provided that the zero– point is fixed inde...

Perturbation Theory of W*-Dynamics, Liouvilleans and KMS-States

Kms States on the Square of White Noise Algebra

It was shown in [AFS00] that there are only three types of irreducible unitary representations θ of sl2. Using the Schurmann triple one can associate with each θ a number of representations of the square of white noise (SWN) algebra A. However, in analogy with the Boson, Fermion and q-deformed case, we expect that some interesting non irreducible representations of sl2 may result in GNS represe...

Conformal Measures for Rational Functions

We show that the set of conical points of a rational function of the Riemann sphere supports at most one conformal measure. We then study the problem of existence of such measures and their ergodic properties by constructing Markov partitions on increasing subsets of sets of conical points and by applying ideas of the thermodynamic formalism. 1 Introduction. In this paper we recall from U2] the...

Kms States of Quasi-free Dynamics on Pimsner Algebras

A continuous one-parameter group of unitary isometries of a right-Hilbert C*bimodule induces a quasi-free dynamics on the Cuntz-Pimsner C*-algebra of the bimodule and on its Toeplitz extension. The restriction of such a dynamics to the algebra of coefficients of the bimodule is trivial, and the corresponding KMS states of the Toeplitz-Cuntz-Pimsner and Cuntz-Pimsner C*-algebras are characterize...