A Note on Eigenvalues of Liouvilleans
Pillet, Claude-Alain ; Jaksic, Vojkan
HAL, hal-00005460 / Harvested from HAL
Text on HAL
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.
Publié le : 2001-07-05
Classification:  quantum statistical mechanics,  weak mixing,  spectral theory,  ergodic theory,  Liouvillean,  [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech],  [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph],  [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA],  [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP] 
@article{hal-00005460,
     author = {Pillet, Claude-Alain and Jaksic, Vojkan},
     title = {A Note on Eigenvalues of Liouvilleans},
     journal = {HAL},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00005460}
}

Pillet, Claude-Alain; Jaksic, Vojkan. A Note on Eigenvalues of Liouvilleans. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00005460/