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university of Provence - Aix-Marseille I |  |
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university of Provence - Aix-Marseille I | |
| HAL: hal-00005460, version 1 |
| DOI: 10.1023/A:1013561529682 |
| Detailed view |  Export this paper |
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| Journal of Statistical Physics 105 (2001) 937 - 941 |
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| A Note on Eigenvalues of Liouvilleans |
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| Claude-Alain Pillet 1Vojkan Jaksic 2 |
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| (2001) |
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| 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. |
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| 1: | Centre de Physique Théorique (CPT) |
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CNRS : FR2291 – Université de Provence - Aix-Marseille I – Université de la Méditerranée - Aix-Marseille II – Université Sud Toulon Var |
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| 2: | Department of Mathematics and Statistics [Mac Gill] |
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Mac Gill University |
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| Subject | : | Physics/Condensed Matter/Statistical Mechanics Physics/Physics/General Physics Mathematics/Operator Algebras Mathematics/Spectral Theory |
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| Liouvillean – ergodic theory – spectral theory – weak mixing – quantum statistical mechanics |
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| 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 | |
