1. Decoherence and Classical dynamics in Markovian Quantum Open Systems O. Brodier (1) A. M. Ozorio de Almeida (2) (1)M.P.I.P.K.S. Dresden, ALLEMAGNE (2)C.B.P.F. Rio de Janeiro, BRASIL

2. Phase Space Representation Classical propagation Quantum propagation Liouville propagation: Wigner function: S. Habib, K. Shizume, W. H. Zurek Phys.Rev.Lett. 80 (1998) 4361-4365

3. Separation time Z. P. Karkuszewski, J. Zakrzewski, W. H. Zurek Phys. Rev. A 65, 042113 (2002)

4. Decoherence due to coupling to environment: effect on separation time?

5. Characteristic function Momenta: Semiclassical analysis: Markovian Quantum Open System: Hamilton Jacobi:

6. Result with

7. Conclusion analysis of decoherence of a Markovian Quantum Open System Dynamical dependence of decoherence A.M. Ozorio de Almeida, O. Brodier in press Ann. Phys. (2006)

8. W.K.B.

9. Entanglement dynamics A B A B Measuring environment → Pure entanglement Entanglement of a mixture

10. Setup 1 A B

11. Setup 2 A B

12. Conclusion For this example there exists an optimal experimental setup which gives the exact entanglement measure. General Prescription for Measuring Environment?