1. Dynamics of complex quantum systems Denis Lacroix –CNRS-GANIL lacroix@ganil.fr ESNT “Les Jeunots…”, Saclay 4-7 Feb. 2008 Phenomenology of nuclear reactions Ab-initio methods in open and closed systems

2. Topics developed : phenomenology of nuclear dynamics Fusion reactions … and beyond 3D TDHF Chomaz, Bonche Simenel, Washiyama (Postdoc), Yilmaz (Postdoc) Coll. : Mean-field theories Theoretical tools Spherical or 3D HF/TDHF at finite T T=cte Contraint mean-field Q=r 2 Link static/dynamics Chomaz Coll. :

3. Beyond mean-field Theoretical tools RPA + 2p2h+ph*phonons Inclusion of dissipation and fluctuations Coll. : Ayik, Chomaz Inclusion of pairing effect Coll. : TDHFB, TDDM Simenel, Duguet Assié (PhD), Avez (PhD) Inclusion of long-range correlation/conf mixing TD-GCM under dev. Coll. : Goutte, Simenel V(Q) Shape coexistence Configuration mixing within Energy Density Functional Coll. : Bender, Duguet GQR

4. Models dedicated to experiments Theoretical tools Scarpaci, Assié (PhD) Fallot, Lima Nuclear Break-up 3D Time Dep. Schrödinger Eq. Coll. : time HIPSE/n-IPSE Macroscopic/Microscopic model (can be downloaded on the web) Multifragmentation/Spallation reac. Coll. :Durand, Lopez, Vient, Léhaut (PhD), Tsang,Yennello… Mass Yield Mass HIPSE EPAX DATA AMD

5. Exact Monte-Carlo methods for open and closed systems

6. Highlight : Theory of open quantum systems Environment System Projection technique Weak coupling approx. Markovian approx. At t=0 Approximate Dissipative dynamics Gardiner and Zoller, Quantum noise (2000) Breuer and Petruccione, The Theory of Open Quant. Syst. Can be simulated by stochastic eq. on |  >, The Master equation being recovered using : Lindblad master equation: Exact dynamics with SSE on simple state Then, the average dyn. identifies with the exact one 1 For total wave For total density 2 D. Lacroix, PRA72 (2005)

7. Average density The dynamics of the system+environment can be simulated exactly with quantum jumps (or SSE) between “simple” state. Exact dynamics of a systems coupled to an environment with SSE Environment System Hamiltonian { with A stochastic version Exact dynamics At t=0 time Average evolution + +

8. A simple illustration: spin systems Lacroix, Phys. Rev. A72, 013805 (2005). A two-level system interacting with a bath of spin systems environment system System P P Coupling Introduction of mean-field: H mean-field + “Noise” Direct application of SSE: H “Noise” Occupation probability time 1000 trajectories Exact evolution Average over Stochastic evolution Occupation probability time 0 0.51.01.5 Stochastic equation are not unique. One can take advantage of this flexibility (mean-field)

9. System space Exact evolution Environment Relevant degrees of freedom: system Recent advances : exact projected dynamics Lacroix, submitted to PRL (2008) Exact master equation for open quantum systems Example : system + environment Indept.evol. Mean-field Non-local in time drift noise

10. Application : spin-boson model + heat bath  z =+1  z =-1   Leggett et al, Rev. Mod. Phys (1987) Coupling System + bath weak coupling strong coupling Result (2000 trajectories) Stockburger, Grabert, PRL (2002) Comparison with related work : Path integrals + influence functional Zhou et al, Europhys. Lett. (2005) 2 24 traj. !

11. From open to closed Many-Body interacting systems System space Exact evolution Environment Open systems One Body space Exact evolution Missing information Closed systems Slater det., Quasi-particle,… D. Lacroix, Annals of Physics, 322 (2007).

12. Speculative summary : where we go in dyn. Mean-field models? Theory of open and closed systems : Interdisciplinarity Formal aspects of open quantum systems Ab-initio methods for interacting bosons and fermions And nuclear Physics ? Ab-initio methods for infinite syst. And nuclear Structure ? Dynamical Theories Beyond mean-field ? What does it mean? Cf: Energy Dens. Func. Should we stop the dev. of reaction models based on mean-field ? We should definitively define what we are doing (Energy Density Functional)! New perspective for/from Time-Dependent DFT Non-locality in time / causality in mean-field like approximations