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<title>Theory of Cluster Dynamics</title>
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<li style="margin-top:1px;border-top:1px solid #B0C4DE; "><a href="index.html">Home</a></li>
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<li><a href="intro.html">Introductory Overview</a></li>
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<li><a href="research.html">Scientific Information</a></li>
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<li><a href="staff.html">Staff</a></li>
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<li><a href="publications.html">Publications/Talks</a></li>
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<p><font size="6" color="white"><b>Theory of Cluster Dynamics</b></font><font
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size="5"><br />
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</font><font size="6"> </font><font size="5">The Toulouse -
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Erlangen Collaboration</font></p>
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<div id="contentBoxHeader">
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<p>Our Research Activities</p>
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--> </div>
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<div id="contentBoxWide"><!--
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<div style="width:250px;float:left;"> <div id="cBoxEnv">
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<div id="cBoxHeader"> A popular guide
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</div> <div id="cBoxContent">
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<p>
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For non-experts we provide some interesting basic and popular information on our research activities: </p>
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<ul> <li>
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<p><a href="intro.html">What are clusters?</a></p> </li>
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<li> <p><a href="dynamics.html">Why studying cluster dynamics?</a></p>
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</li> <li>
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<p><a href="ourdynamics/our_dynamics.html">How we deal with cluster dynamics</a></p> </li>
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</ul>
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</div>
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</div> </div>
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-->
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<div style="width: 770px; float: left;">
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<div id="cBoxEnv">
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<div id="cBoxHeader"> A scientific guide </div>
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<div id="cBoxContent">
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<div style="text-align: justify;"> </div>
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<div id="cBoxContent">
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<div style="text-align: justify;"> </div>
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<p style="text-align: justify;">The core of our activities
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concerns
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the theoretical analysis of the dynamics of molecules and
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clusters.
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The method of choice for most of our studies is
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time-dependent density
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functional theory. One can sort our activities along three
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major
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directions of research: intrinsic dynamical system
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properties
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investigated with moderate external excitations
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(perturbative regime),
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response to strong external fields analyzed with a bunch of
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different
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observables taking care particularly of information from
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electron
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emission, and development of the necessary numerical as well
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as
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theoretical tools. The majority of applications deals with
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free
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molecules and clusters. One branch of studies deals also
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with clusters
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in contact with polarizable media (raregas matrices,
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insulating
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surfaces).
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</p>
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<p><b><a href="tddft-md/formal.html">Theoretical developments</a>
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</b></p>
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<p style="text-align: justify;">Understanding of cluster
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dynamics
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requires elaborate theoretical tools.
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Time-Dependent Density Functional Theory (TDDFT) represents
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here a robust starting point
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which allows to address a great variety of situations. We
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use TDDFT at various
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levels of sophistication. Basis is the most efficient<a href="tddft-md/formal.html">,
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Time-Dependent
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Local-Density Approximation (TDLDA)</a>. It is augmented
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by
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a Self-Interaction Correction (SIC) for a proper description
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of
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electron emission and associated observables. Ionic motion
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is
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propagated simultaneously by classical Molecular Dynamics
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(MD)
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amounting together to TDLDA-MD. Very energetic processes
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allow
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semi-classical approximations for which we use mostly the
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Vlasov-LDA
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approximation. The latter allows a relatively simple
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extension by
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dynamical correlations with a collision term which accounts
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properly
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for the Pauli principle leading to the
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Vlasov-Uehling-Uhlenbeck (VUU)
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equation. <br />
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Recent developments focus on the implementation of such
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dynamical correlations in the fully quantum mechanical
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framework of
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TDLDA. A robust, phenomenological route is followed with the
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Relaxation-Time Approximation (RTA) known from bulk matter
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and
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implemented now for finite Fermion systems. An exact
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evaluation of the
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quantum-mechanical collision is prohibitively expensive.
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With
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Stochastic TDLDA (STDLDA), we render the case manageable by
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a
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stochastic evaluation of the collisions. Full STDLDA can
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cope even
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with large fluctuations of the mean field as they are
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typical for
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violent dynamical processes. Further savings are possible in
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the
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regime of small statistical fluctuations which allows to use
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one
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average mean field delivering Average STDLDA (ASTDLDA). In
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any case,
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the dynamical correlations thus implemented allow a
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pertinent
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description of dissipation in electron dynamics which
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becomes an
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important ingredient at longer times (in metal clusters
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typically > 50
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fs). <br />
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Numerically, we solve TDLDA and related approaches in
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coordinate-space grid representations, fully
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three-dimensional if
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necessary and in the much faster cylindrically symmetric 2D
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grid if
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the case allows. All grids are surrounded bands generating
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absorbing
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boundary conditions to allow a correct description and
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analysis of
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electron emission.
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</p>
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<p>
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<b><a href="analysis/detail1.html">Intrinsic dynamical
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properties of molecules and clusters
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</a></b>
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</p>
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<p style="text-align: justify;">At moderate perturbations, the
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system
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response dominantly reflects its own (structure and
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dynamical)
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properties. The most prominent feature is the optical
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response which
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characterizes the coupling of photons to the electrons of
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the
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system. We obtain it from TDLDA driven in the regime of weak
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perturbations [<a href="publications.html#Cal97">Cal97</a>]. As optical
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response is the doorway to almost all further dynamical
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processes, it
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is regularly scanned before starting with more involved
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scenarios (see
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below).
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<br />
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The ionic dynamics of molecules and clusters is explored by
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pump and
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probe scenarios, again driven in the regime of moderate
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excitations to
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explore the system as such without too much perturbation.
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</p>
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<p>
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<b><a href="analysis/detail2.html">
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Free clusters in strong external fields</a></b></p>
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<p style="text-align: justify;">
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When applying stronger external fields, a world of dynamical
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scenarios
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is opened as, e.g., multi-photon ionization, higher harmonic
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generation, multi-fragmentation, or Coulomb explosion [<a href="publications.html#Fen10">Fen10</a>]. <br />
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A large part of our activities is concerned with dynamical
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information
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which can be obtained from electron emission. The simplest
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and most
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widely used observable is the net ionization, often in
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connection with
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time resolved measurements. The trends of ionization with
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systematically varied laser parameters (frequency,
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intensity, pulse
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length, delay times) contain already a lot of valuable
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information. More can be obtained by looking at the emitted
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electrons
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in detail collecting the distributions of kinetic energies,
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called
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Photo-Electron Spectra (PES), or angular directions, in the
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ideal case
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even both together as Angular Resolved PES (ARPES). Our
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numerical
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tools (coordinate-space representation with absorbing
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boundary
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conditions) to solve TDLDA allow a rather convenient
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computation of
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all these detailed distributions, if needed even in time
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resolved
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manner. We apply them to simulate measurements in raregas
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atom, metal
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clusters, and C<sub>60</sub> [<a href="publications.html#Wop15">Wop15</a>].
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<br />
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The detailed distributions ARPES indicate indicate
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limitations of a
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mere mean-field description as in TDLDA. They overestimate,
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e.g., the
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forward/backward emission along the laser polarization axis.
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This
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calls for dissipation in electron dynamics as it is given by
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dynamical
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correlations. This is the main line of present development
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and
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applications. <br />
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</p>
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<p><b><a href="tddft-md/detailQMMM.html">Molecules and
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clusters in
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contact with a polarizable environment</a></b>
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</p>
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<p style="text-align: justify;">Clusters can be more easily
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handled
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experimentally when they are produced in contact with an
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environment
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(deposited on a surface or embedded in a matrix). Thus a
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large amount
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experimental data was produced under these conditions. We
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have thus
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developed a simplified description of the environment in
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terms of
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classical Molecular Mechanics (MM) taking care to include a
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proper
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modeling of its dynamical polarizability. This is coupled to
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the
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standard Quantum-Mechanical (QM) handling of the electron
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cloud in the
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active molecule or cluster, yielding together QM/MM method.
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This
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hierarchical approach allows us to explore various dynamical
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scenarios, as optical response of deposited clusters,
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deposition
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processes, irradiation of embedded clusters by an intense
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laser field,
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etc with sufficiently large samples for the environment [<a href="publications.html#Din09">Din09</a>].
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</p>
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</div>
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<p style="text-align: justify;"></p>
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