Transcript Diapositive 1

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