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Dynamics of complex quantum systems

Dynamics of complex quantum systems. Denis Lacroix –CNRS-GANIL lacroix@ganil.fr. Ab-initio methods in open and closed systems. Phenomenology of nuclear reactions. ESNT “Les Jeunots…”, Saclay 4-7 Feb. 2008. Contraint mean-field Q=r 2. T= c te.

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Dynamics of complex quantum systems

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

  2. Contraint mean-field Q=r2 T=cte Topics developed : phenomenology of nuclear dynamics Theoretical tools Mean-field theories Link static/dynamics Spherical or 3D HF/TDHF at finite T Chomaz Coll. : Fusion reactions 3D TDHF Coll. : Chomaz, Bonche Simenel, Washiyama (Postdoc), Yilmaz (Postdoc) … and beyond

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

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

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

  6. Environment System Approximate Dissipative dynamics At t=0 Projection technique Weak coupling approx. Markovian approx. Lindblad master equation: 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. Highlight : Theory of open quantum systems Exact dynamics with SSE on simple state Then, the average dyn. identifies with the exact one For total wave 1 For total density 2 D. Lacroix, PRA72 (2005)

  7. Hamiltonian Environment Exact dynamics System time 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 Exact dynamics of a systems coupled to an environment with SSE

  8. A two-level system interacting with a bath of spin systems system 1000 trajectories Average over Stochastic evolution environment Occupation probability Direct application of SSE: Exact evolution H “Noise” 0.5 1.0 1.5 0 time Introduction of mean-field: Occupation probability Coupling System H mean-field + “Noise” time Stochastic equation are not unique. One can take advantage of this flexibility (mean-field) P P A simple illustration: spin systems Lacroix, Phys. Rev. A72, 013805 (2005).

  9. <B> Exact evolution Environment <S2> Relevant degrees of freedom: system <S1> System space Recent advances : exact projected dynamics Lacroix, submitted to PRL (2008) Example : system + environment Exact master equation for open quantum systems Indept .evol. drift Mean-field Non-local in time noise

  10. Application : spin-boson model + heat bath Leggett et al, Rev. Mod. Phys (1987) System + bath D0 e Coupling sz=-1 sz=+1 Comparison with related work : Path integrals + influence functional Result (2000 trajectories) Zhou et al, Europhys. Lett. (2005) strong coupling 224 traj. ! weak coupling Stockburger, Grabert, PRL (2002)

  11. <B> <B> Exact evolution Missing information Exact evolution Environment <S2> <A2> <S1> <A1> System space One Body space From open to closed Many-Body interacting systems Closed systems Open 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 ? 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 What does it mean? Cf: Energy Dens. Func. Ab-initio methods for infinite syst. And nuclear Structure ? Dynamical Theories Beyond mean-field ? Should we stop the dev. of reaction models based on mean-field ?

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