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Dynamics of complex quantum systems Denis Lacroix –CNRS-GANIL [email protected] Phenomenology of nuclear reactions Ab-initio methods in open and closed systems ESNT “Les Jeunots…”, Saclay 4-7 Feb. 2008 Topics developed : phenomenology of nuclear dynamics Theoretical tools Mean-field theories Link static/dynamics Contraint mean-field Q=r2 T=cte Spherical or 3D HF/TDHF at finite T Coll. : Chomaz Fusion reactions 3D TDHF Coll. : Chomaz, Bonche Simenel, Washiyama (Postdoc), Yilmaz (Postdoc) … and beyond Beyond mean-field Theoretical tools Inclusion of dissipation and fluctuations GQR RPA + 2p2h+ph*phonons Coll. : Ayik, Chomaz Inclusion of pairing effect TDHFB, TDDM Coll. : Simenel, Duguet Assié (PhD), Avez (PhD) Inclusion of long-range correlation/conf mixing TD-GCMunder dev. V(Q) Shape coexistence Coll. : Goutte, Simenel Configuration mixing within Energy Density Functional Coll. : Bender, Duguet Models dedicated to experiments Theoretical tools Nuclear Break-up 3D Time Dep. Schrödinger Eq. Coll. : Scarpaci, Assié (PhD) Fallot, Lima time Multifragmentation/Spallation reac. HIPSE/n-IPSE Macroscopic/Microscopic model (can be downloaded on the web) Mass Yield AMD HIPSE DATA Mass EPAX Coll. : Durand, Lopez, Vient, Léhaut (PhD), Tsang,Yennello… Exact Monte-Carlo methods for open and closed systems Highlight : Theory of open quantum systems Environment System Approximate Dissipative dynamics At t=0 Weak coupling approx. Exact dynamics with SSE on simple state Projection technique Markovian approx. Lindblad master equation: Then, the average dyn. identifies with the exact one Can be simulated by stochastic eq. on |F>, The Master equation being recovered using : Gardiner and Zoller, Quantum noise (2000) Breuer and Petruccione, The Theory of Open Quant. Syst. 1 For total wave 2 For total density D. Lacroix, PRA72 (2005) Exact dynamics of a systems coupled to an environment with SSE Hamiltonian Environment System Exact dynamics At t=0 A stochastic version { with Average evolution + + The dynamics of the system+environment can be simulated exactly with quantum jumps (or SSE) between “simple” state. Average density A simple illustration: spin systems Lacroix, Phys. Rev. A72, 013805 (2005). A two-level system interacting with a bath of spin systems system 1000 trajectories H “Noise” Coupling Introduction System of mean-field: P H mean-field + “Noise” P Average over Stochastic evolution Occupation probability Direct application of SSE: Occupation probability environment Exact evolution 0 0.5 1.0 time time Stochastic equation are not unique. One can take advantage of this flexibility (mean-field) 1.5 Recent advances : exact projected dynamics Lacroix, submitted to PRL (2008) <B> Exact evolution <S2> <S1> Relevant degrees of freedom: system Example : system + environment Exact master equation for open quantum systems Indept .evol. Mean-field Non-local in time drift noise Application : spin-boson model + heat bath Leggett et al, Rev. Mod. Phys (1987) System + bath D0 e sz=+1 Coupling sz=-1 Result (2000 trajectories) strong coupling Comparison with related work : Path integrals + influence functional Zhou et al, Europhys. Lett. (2005) 224 traj. ! weak coupling Stockburger, Grabert, PRL (2002) From open to closed Many-Body interacting systems Closed systems Open systems Slater det., Quasi-particle,… <B> Exact evolution <B> Exact evolution <S2> <A2> <S1> <A1> D. Lacroix, Annals of Physics, 322 (2007). 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