4462 articles – 13150 references  [version française]
 HAL: hal-00005460, version 1
 Journal of Statistical Physics 105 (2001) 937 - 941
 A Note on Eigenvalues of Liouvilleans
 (2001)
 Let L be the Liouvillean of an ergodic quantum dynamical system $(\mathfrak{M} ,\tau,\omega)$. We give a new proof of the theorem of Jadczyk that eigenvalues of L are simple and form a subgroup of $\mathbb{R}$ . If $\omega$ is a $(\tau, \beta)$-KMS state for some $\beta>0$ we show that this subgroup is trivial, namely that zero is the only eigenvalue of L. Hence, for KMS states ergodicity is equivalent to weak mixing.
 1: Centre de Physique Théorique (CPT) CNRS : FR2291 – Université de Provence - Aix-Marseille I – Université de la Méditerranée - Aix-Marseille II – Université Sud Toulon Var 2: Department of Mathematics and Statistics [Mac Gill] Mac Gill University
 Subject : Physics/Condensed Matter/Statistical MechanicsPhysics/Physics/General PhysicsMathematics/Operator AlgebrasMathematics/Spectral Theory
 Keyword(s): Liouvillean – ergodic theory – spectral theory – weak mixing – quantum statistical mechanics
 hal-00005460, version 1 http://hal.archives-ouvertes.fr/hal-00005460 oai:hal.archives-ouvertes.fr:hal-00005460 From: Claude-Alain Pillet <> Submitted on: Sunday, 19 June 2005 16:45:41 Updated on: Sunday, 19 June 2005 16:45:41