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QUANTUM DYNAMICAL SEMIGROUP AND ITS ASYMPTOTIC BEHAVIORS

  • Choi, Veni
  • Published : 2004.02.01

Abstract

In this study we consider quantum dynamical semi-group with a normal faithful invariant state. A quantum dynamical semigroup $\alpha\;=\;\{{\alpha}_t\}_{t{\geq}0}$ is a class of linear normal identity-preserving mappings on a von Neumann algebra M with semigroup property and some positivity condition. We investigate the asymptotic behaviors of the semigroup such as ergodicity or mixing properties in terms of their eigenvalues under the assumption that the semigroup satisfies positivity. This extends the result of [13] which is obtained under the assumption that the semi group satisfy 2-positivity.

Keywords

quantum dynamical semigroup;positivity;Schwarz inequality;Jordan product;ergodicity;weak mixing

References

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Cited by

  1. A Survey on Invariance and Ergodicity of Quantum Markov Semigroups vol.32, pp.3, 2014, https://doi.org/10.1080/07362994.2014.897136
  2. Recurrence and Transience of Quantum Markov Semigroups vol.33, pp.1, 2015, https://doi.org/10.1080/07362994.2014.968287